×

zbMATH — the first resource for mathematics

Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture. (English. Russian original) Zbl 1187.22014
J. Math. Sci., New York 159, No. 5, 653-751 (2009); translation from Fundam. Prikl. Mat. 13, No. 7, 85-225 (2007).
A map \(T\) from a group \(G\) to the algebra \(L(E)\) of bounded operators on a Banach space \(E\) is called a quasirepresentation if there exists \(\varepsilon>0\) such that \(\|(T(gh)-T(g)T(h))x\|\leq\varepsilon\|x\|\) for any \(g,h\in G\), \(x\in E\). A description of the structure of all finite-dimensional, locally bounded quasirepresentations of arbitrary connected Lie groups is given. The paper is nicely written and contains a lot of examples and related results, including a generalization of the van der Waerden theorem on automatic continuity for group representations and the proof of Mishchenko’s conjecture on the oscillation of discontinuous representations at the identity element of a group.

MSC:
22E46 Semisimple Lie groups and their representations
47D03 Groups and semigroups of linear operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] M. Abel and K. Jarosz, ”Small deformations of topological algebras,” Stud. Math., 156, No. 3, 202–226 (2003). · Zbl 1031.46054
[2] J. Araujo and K. Jarosz, ”Separating maps on spaces of continuous functions,” in: Function Spaces. Proc. 3rd Conf., Edwardsville, IL, 1998, Contemp. Math., Vol. 232, Amer. Math. Soc., Providence (1999), pp. 33–37. · Zbl 0937.46021
[3] R. W. Bagley, T. S. Wu, and J. S. Yang, ”Pro-Lie groups,” Trans. Amer. Math. Soc., 287, No. 2, 829–838 (1985). · Zbl 0575.22006
[4] J. W. Baker and B. M. Lashkarizadeh, ”Representations and positive definite functions on topological semigroups,” Glasgow Math. J., 38, No. 1, 99–111 (1996). · Zbl 0845.22003
[5] J. Baker, J. Lawrence, and F. Zorzitto, ”The stability of equation f(xy) = f(x)f(y),” Proc. Amer. Math. Soc., 74, No. 2, 242–246 (1979). · Zbl 0397.39010
[6] S. Banach, Théorie des Opérations Linéaires, Monogr. Mat., PWN, Warszaw (1932).
[7] A. Banyaga, ”Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique,” Comment. Math. Helv., 53, No. 2, 174–227 (1978). · Zbl 0393.58007
[8] J. Barge and E. Ghys, ”Surfaces et cohomologie bornée,” Invent. Math., 92, 509–526 (1988). · Zbl 0641.55015
[9] J. Barge and E. Ghys, ”Cocycles d’Euler et de Maslov,” Math. Ann., 294, No. 2, 235–265 (1992). · Zbl 0894.55006
[10] C. Bavard, ”Longueur stable des commutateurs,” Enseign. Math., 37, 109–150 (1991). · Zbl 0810.20026
[11] E. J. Beggs, Pointwise Bounded Asymptotic Morphisms and Thomsen’s Non-Stable k-Theory, arXiv:math.OA/0201051 (2002).
[12] M. B. Bekka, P. de la Harpe, and A. Valette, Kazhdan’s Property (T), http://perso.univ-rennes1.fr/bachir.bekka/KazhdanTotal.pdf (2004)
[13] G. Besson, Sur la Cohomologie Bornée, Report, Séminaire cohomologie bornée, Éc. Norm. Sup. Lyon (Février 1988).
[14] P. Biran, M. Entov, and L. Polterovich, ”Calabi quasimorphisms for the symplectic ball,” Commun. Contemp. Math., 6, No. 5, 793–802 (2004). · Zbl 1076.53110
[15] B. Blackadar and E. Kirchberg, ”Generalized inductive limits of finite-dimensional C*-algebras,” Math. Ann., 307, No. 3, 343–380 (1997). · Zbl 0874.46036
[16] A. Borel, ”Sections locales de certains espaces fibrés,” C. R. Acad. Sci. Paris, 230, 1246–1248 (1950). · Zbl 0041.52004
[17] A. Bouarich, ”Suites exactes en cohomologie bornée réelle des groups discrets,” C. R. Acad. Sci. Paris, 320, 1355–1359 (1995). · Zbl 0833.57023
[18] N. Bourbaki, Lie Groups and Lie Algebras. Chapters 7–9, Springer, Berlin (2005). · Zbl 1139.17002
[19] R. Brooks, ”Some remarks on bounded cohomology,” in: Riemann Surfaces and Related Topics, Proc. 1978 Stony Brook Conf., State Univ. New York, Stony Brook, NY, 1978, Ann. Math. Stud., Vol. 97, Princeton Univ. Press, Princeton (1981), pp. 53–63.
[20] L. G. Brown, ”Continuity of actions of groups and semigroups on Banach spaces,” J. London Math. Soc. (2), 62, No. 1, 107–116 (2000). · Zbl 0957.22002
[21] L. G. Brown, R. G. Douglas, and P. A. Fillmore, ”Extensions of C*-algebras and K-homology,” Ann. Math., 105, No. 2, 265–324 (1977). · Zbl 0376.46036
[22] L. G. Brown and N. C. Wong, ”Unbounded disjointness preserving linear functionals,” Monatsh. Math., 141, No. 1, 21–32 (2004). · Zbl 1046.46039
[23] J. Brzdek, ”On orthogonally exponential and orthogonally additive mappings,” Proc. Amer. Math. Soc., 125, 2127–2132 (1997). · Zbl 0870.39011
[24] T. Bühler, Gromov’s Geodesic Flow, Diplomarbeit, ETZ: Zürich (2002).
[25] M. Burger and A. Iozzi, ”Boundary maps in bounded cohomology,” Geom. Funct. Anal., 12, No. 2, 281–292 (2002). · Zbl 1006.22011
[26] M. Burger and N. Monod, ”Continuous bounded cohomology and applications to rigidity theory,” Geom. Funct. Anal., 12, No. 2, 219–280 (2002). · Zbl 1006.22010
[27] M. Burger and N. Monod, ”On and around the bounded cohomology of SL2,” in: Rigidity in Dynamics and Geometry, Contrib. from the Programme Ergodic Theory, Geometric Rigidity and Number Theory, Isaac Newton Inst. for the Math. Sci., Cambridge, January 5–July 7, 2000, Springer, Berlin (2002), pp. 19–37.
[28] R. C. Busby, ”Double centralizers and extensions of C*-algebras,” Trans. Amer. Math. Soc., 132, No. 1, 79–99 (1968). · Zbl 0165.15501
[29] E. Calabi, ”On the group of automorphisms of a symplectic manifold,” Problems in Analysis (Lectures at the Symp. in Honor of Salomon Bochner, Princeton Univ., Princeton, N.J., 1969 ), Princeton Univ. Press, Princeton (1970), pp. 1–26.
[30] M. Cambern, ”On isomorphisms with small bound,” Proc. Amer. Math. Soc., 18, 1062–1066 (1967). · Zbl 0165.47402
[31] É. Cartan, ”Les groupes réels simples, finis et continus,” Ann. Sci. École Norm. Sup. (3), 31, 263–355 (1914). · JFM 45.1408.03
[32] E. Christensen, ”Close operator algebras,” in: Deformation Theory of Algebras and Structures and Applications, NATO Adv. Study Inst., Castelvecchio–Pascoli/Italy, 1986, NATO ASI Ser., Ser. C, Math. Phys. Sci., Vol. 247, Kluwer Academic, Dordrecht (1988), pp. 537–556.
[33] E. Christensen, E. G. Effros, and A. Sinclair, ”Completely bounded multilinear maps and C*-algebraic cohomology,” Invent. Math., 90, No. 2, 279–296 (1987). · Zbl 0646.46052
[34] A. Connes, M. L. Gromov, and H. Moscovici, ”Conjecture de Novikov et fibrés presque plats,” C. R. Acad. Sci. Paris, Sér. I Math., 310, No. 5, 273–277 (1990). · Zbl 0693.53007
[35] A. Connes and N. Higson, Almost homomorphisms and KK-theory, http://www.math.psu.edu/higson/Papers/ch1.pdf (1989).
[36] A. Connes and N. Higson, ”Déformations, morphismes asymptotiques et K-théorie bivariante,” C. R. Acad. Sci. Paris, Sér. I Math., 311, No. 2, 101–106 (1990). · Zbl 0717.46062
[37] G. Corach and J. E. Galé, ”On amenability and geometry of spaces of bounded representations,” J. London Math. Soc. (2), 59, No. 1, 311–329 (1999). · Zbl 0922.46044
[38] J. Cuntz, ”Bivariante K-Theorie für lokalkonvexe Algebren und der bivariante Chern–Connes-Charakter,” Doc. Math., 2, 139–182 (1997). · Zbl 0920.19004
[39] J. Cuntz, Bivariant K-Theory and the Weyl Algebra, arXiv:math.KT/0401295 (2004).
[40] M. Dadarlat and S. Eilers, ”Asymptotic unitary equivalence in KK-theory,” K-Theory, 23, 305–322 (2001). · Zbl 0991.19002
[41] H. G. Dales, F. Ghahramani, and A. Ya. Helemskii, ”The amenability of measure algebras,” J. London Math. Soc. (2), 66, No. 1, 213–226 (2002). · Zbl 1015.43002
[42] H. G. Dales and A. R. Villena, ”Continuity of derivations, intertwining maps, and cocycles from Banach algebras,” J. London Math. Soc. (2), 63, No. 2, 215–225 (2001). · Zbl 1023.46050
[43] S. G. Dani and C. R. E. Raja, ”Asymptotics of measures under group automorphisms and an application of factor sets,” in: Lie Groups and Ergodic Theory. Proc. Int. Colloq., Mumbai, India, January 4–12, 1996, Tata Inst. Fundam. Res. Stud. Math., Vol. 14, Narosa Publ. Hause, New Delhi (1998), pp. 59–73. · Zbl 0945.43001
[44] M. M. Day, Normed Linear Spaces, Ergebnisse Math. ihrer Grenzgebiete, Vol. 21, Springer, Berlin (1958). · Zbl 0082.10603
[45] G. Debs and J. Saint Raymond, ”Compact covering mappings between Borel sets and the size of constructible reals,” Trans. Amer. Math. Soc., 356, No. 1, 73–117 (2004). · Zbl 1051.03037
[46] R. Dedekind, ”Erlauterungen zu den Fragmenten, XXVIII,” in: Collected Works of Bernhard Riemann, Dover, New York (1953), pp. 466–478.
[47] J. Dixmier, C*-Algèbres et Leurs Réprésentations, Dunod, Paris (1969).
[48] J. Duncan and S. A. R. Hosseiniun, ”The second dual of a Banach algebra,” Proc. Roy. Soc. Edinburgh Sect. A, 19, 309–325 (1979). · Zbl 0427.46028
[49] N. Dunford and J. T. Schwartz, Linear Operators, Part I, General Theory, Wiley–Interscience, New York (1988). · Zbl 0635.47001
[50] J.-L. Dupont, ”Simplicial de Rham cohomology and characteristic classes of flat bundles,” Topology, 15, 233–245 (1976). · Zbl 0331.55012
[51] E. G. Effros and Z.-J. Ruan, Operator Spaces, London Math. Soc., New Ser., Vol. 23, Clarendon Press, Oxford Univ. Press, Oxford (2000).
[52] S. Eilers and T. A. Loring, ”Computing contingencies for stable relations,” Internat. J. Math., 10, No. 3, 301–326 (1999). · Zbl 1039.46506
[53] G. A. Elliott and Q. Lin, ”Cut-down method in the inductive limit decomposition of non-commutative tori,” J. London Math. Soc. (2), 54, No. 1, 121–134 (1996). · Zbl 0857.46046
[54] R. Engelking, General Topology, Heldermann, Berlin (1989).
[55] M. Entov, ”Commutator length of symplectomorphisms,” Comment. Math. Helv., 79, 58–104 (2004). · Zbl 1048.53056
[56] M. Entov and L. Polterovich, ”Calabi quasimorphism and quantum homology,” Internat. Math. Res. Notices, 30, 1635–1676 (2003). · Zbl 1047.53055
[57] R. Exel and M. Laca, ”Continuous Fell bundles associated to measurable twisted actions,” Proc. Amer. Math. Soc., 125, No. 3, 795–799 (1997). · Zbl 0870.46044
[58] R. Exel and T. A. Loring, ”Invariants of almost commuting unitaries,” J. Funct. Anal., 95, No. 2, 364–376 (1991). · Zbl 0748.46031
[59] R. Eymard, ”L’algèbre de Fourier d’un groupe localement compact,” Bull. Soc. Math. France, 92, 181–236 (1964). · Zbl 0169.46403
[60] V. A. Faiziev, ”Pseudocharacters on free products of semigroups,” Funct. Anal. Appl., 21, No. 1, 77–79 (1987). · Zbl 0625.20056
[61] V. A. Faiziev, ”Pseudocharacters on free groups and on certain group constructions,” Russ. Math. Surv., 43, No. 5, 219–220 (1988). · Zbl 0671.20023
[62] B. L. Feigin and D. B. Fuks, ”Cohomologies of Lie groups and Lie algebras,” in: Lie Groups and Lie Algebras, II, Encycl. Math. Sci., Vol. 21, Springer, Berlin (2000), pp. 125–223. · Zbl 0653.17008
[63] B. E. Forrest and V. Runde, ”Amenability and weak amenability of the Fourier algebra,” Math. Z., 250, 731–744 (2004). · Zbl 1080.22002
[64] G. L. Forti, ”The stability of homomorphisms and amenability, with applications to functional equations,” Abh. Math. Sem. Univ. Hamburg, 57, 215–226 (1987). · Zbl 0619.39012
[65] H. Freudenthal, ”Beziehungen der E7 und E8 zur Oktavebene. I,” Indag. Math., 16, No. 3, 218–230 (1954).
[66] S. A. Gaal, Linear Analysis and Representation Theory, Springer, New York (1973).
[67] J.-M. Gambaudo and É. Ghys, ”Commutators and diffeomorphisms of surfaces,” Ergodic Theory Dynam. Syst., 24, No. 5, 1591–1617 (2004). · Zbl 1088.37018
[68] É. Ghys, ”Groups acting on the circle,” Enseign. Math. (2), 47, No. 3-4, 329–407 (2001). · Zbl 1044.37033
[69] G. Gong and H. Lin, ”Almost multiplicative morphisms and almost commuting matrices,” J. Operator Theory, 40, No. 2, 217–275 (1998). · Zbl 0998.46023
[70] G. Gong and H. Lin, ”Almost multiplicative morphisms and K-theory,” Internat. J. Math., 11, No. 8, 983–1000 (2000). · Zbl 0965.46045
[71] F. P. Greenleaf, Invariant Means on Topological Groups and Their Applications, Van Nostrand Math. Stud., Vol. 16, Van Nostrand, London (1969). · Zbl 0174.19001
[72] R. I. Grigorchuk, ”Some results on bounded cohomology,” in: A. J. Duncan, N. D. Gilbert, and J. Howie, eds., Combinatorial and Geometric Group Theory, Proc. Workshop Held at Heriot-Watt University, Edinburgh, 1993, London Math. Soc. Lect. Note Ser., Vol. 204, pp. 111–163, Cambridge Univ. Press, Cambridge (1995). · Zbl 0853.20034
[73] M. Gromov, ”Volume and bounded cohomology,” Inst. Hautes Études Sci. Publ. Math., 56, 5–99 (1982). · Zbl 0516.53046
[74] M. Gromov, ”Positive curvature, macroscopic dimension, spectral gaps and higher signatures,” in: Functional Analysis on the Eve of the 21st Century, Vol. II, Birkhäuser, Boston (1996), pp. 1–213. · Zbl 0945.53022
[75] N. Gronbak, ”Amenability of weighted convolution algebras on locally compact groups,” Trans. Amer. Math. Soc., 319, No. 2, 765–775 (1990). · Zbl 0701.46035
[76] N. Gronbak, B. E. Johnson, and G. A. Willis, ”Amenability of Banach algebras of compact operators,” Israel J. Math., 87, No. 1–3, 289–324 (1994). · Zbl 0806.46058
[77] K. Grove, H. Karcher, and E. A. Ruh, ”Jacobi fields and Finsler metrics on a compact Lie groups with an application to differential pinching problems,” Math. Ann., 211, No. 1, 7–21 (1974). · Zbl 0282.53047
[78] E. Guentner, N. Higson, and J. Trout, Equivariant E-Theory for C*-Algebras, Mem. Amer. Math. Soc., Vol. 703, Amer. Math. Soc. (2000).
[79] A. Guichardet, Cohomologie des Groupes Topologiques et des Algèbres de Lie, Cedic/Fernand Nathan, Paris (1980). · Zbl 0464.22001
[80] A. Guichardet and D. Wigner, ”Sur la cohomologie réelle des groupes de Lie simples réels,” Ann. Sci. École Norm. Sup. (4), 11, 277–292 (1978). · Zbl 0398.22015
[81] P. de la Harpe, Topics in Geometric Group Theory, Chicago Lect. Math., Univ. of Chicago Press, Chicago (2000). · Zbl 0965.20025
[82] P. de la Harpe and M. Karoubi, ”Représentations approchées d’un groupe dans une algébre de Banach,” Manuscripta Math., 22, No. 3, 293–310 (1977). · Zbl 0371.22007
[83] A. Ya. Helemskii, The Homology of Banach and Topological Algebras, Math. Appl. (Sov. Ser.), Vol. 41, Kluwer Academic, Dordrecht (1989).
[84] A. Ya. Helemskii, Banach and Locally Convex Algebras, Clarendon Press, Oxford Univ. Press, New York (1993).
[85] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York (1962). · Zbl 0111.18101
[86] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Structure of Topological Groups, Integration Theory, Group Representations, Grundlehren Math. Wiss., Vol. 115, Springer, Berlin (1979). · Zbl 0416.43001
[87] N. Higson, ”A primer on KK-theory,” in: Operator Theory: Operator Algebras and Applications, Proc. Summer Res. Inst., Durham, USA, 1988, Proc. Sympos. Pure Math., Vol. 51, Part 1, Amer. Math. Soc., Providence (1990), pp. 239–283.
[88] N. Higson and J. Roe, ”Amenable group actions and the Novikov conjecture,” J. Reine Angew. Math., 519, 143–153 (2000). · Zbl 0964.55015
[89] K.-H. Hofmann and S. A. Morris, The Structure of Compact Groups, Walter de Gruyter, Berlin (1998). · Zbl 0919.22001
[90] K.-H. Hofmann and W. A. F. Ruppert, Lie Groups and Subsemigroups with Surjective Exponential Function, Mem. Amer. Math. Soc., Vol. 618, Amer. Math. Soc. (1997). · Zbl 0889.22001
[91] E. Hotzel, ”Right projective semigroups with 0,” J. Pure Appl. Algebra, 170, No. 1, 35–66 (2002). · Zbl 1008.20051
[92] R. A. J. Howey, ”Approximately multiplicative functionals on algebras of smooth functions,” J. London Math. Soc. (2), 68, No. 3, 739–752 (2003). · Zbl 1064.46032
[93] D. H. Hyers, ”On the stability of the linear functional equation,” Proc. Natl. Acad. Sci. USA, 27, No. 2, 222–224 (1941). · Zbl 0061.26403
[94] D. H. Hyers and T. M. Rassias, ”Approximate homomorphisms,” Aequationes Math., 44, No. 2–3, 125–153 (1992). · Zbl 0806.47056
[95] D. H. Hyers and S. M. Ulam, ”On approximate isometry,” Bull. Amer. Math. Soc., 51, 288–292 (1945). · Zbl 0060.26404
[96] K. Iwasawa, ”On some types of topological groups,” Ann. Math., 50, No. 2, 507–558 (1949). · Zbl 0034.01803
[97] K. Jarosz, Perturbations of Banach Algebras, Lect. Notes Math., Vol. 1120, Springer, Berlin (1985). · Zbl 0557.46029
[98] K. Jarosz, ”Small isomorphisms between operator algebras,” Proc. Edinburgh Math. Soc. (2), 28, No. 2, 121–131 (1985). · Zbl 0577.46013
[99] K. Jarosz, ”Perturbations of function algebras,” in: Deformation Theory of Algebras and Structures and Applications, NATO Adv. Study Inst., Castelvecchio–Pascoli/Italy, 1986, NATO ASI Ser., Ser. C, Math. Phys. Sci., Vol. 247, Kluwer Academic, Dordrecht (1988), pp. 557–563.
[100] K. Jarosz, ”Automatic continuity of separating linear isomorphisms,” Can. Math. Bull., 33, No. 2, pp. 139–144 (1990). · Zbl 0714.46040
[101] K. Jarosz, ”Small perturbations of algebras of analytic functions on polydiscs,” in: Function Spaces, Proc. Conf., Edwardsville (USA) 1990, Lect. Notes Pure Appl. Math., Vol. 136, Marcel Dekker, New York (1992), pp. 223–240. · Zbl 0780.46034
[102] K. Jarosz, ”Almost multiplicative functionals,” Studia Math., 124, No. 1, 37–58 (1997). · Zbl 0897.46043
[103] K. Jarosz, ”When is a linear functional multiplicative?” in: Function Spaces, Proc. 3rd Conf., Edwardsville (USA), May 19–23, 1998, Contemp. Math., Vol. 232, Amer. Math. Soc., Providence (1999), pp. 201–210. · Zbl 0933.46043
[104] B. E. Johnson, ”Approximate diagonals and cohomology of certain annihilator Banach algebras,” Amer. J. Math., 94, 685–698 (1972). · Zbl 0246.46040
[105] B. E. Johnson, Cohomology in Banach Algebras, Mem. Amer. Math. Soc., Vol. 127, Amer. Math. Soc., Providence (1972). · Zbl 0256.18014
[106] B. E. Johnson, ”Perturbations of Banach algebras,” Proc. London Math. Soc. (3), 34, No. 3, 439–458 (1977). · Zbl 0357.46053
[107] B. E. Johnson, ”Approximately multiplicative functionals,” J. London Math. Soc. (2), 34, No. 3, 489–510 (1986). · Zbl 0625.46059
[108] B. E. Johnson, ”Continuity of generalized homomorphisms,” Bull. London Math. Soc., 19, No. 1, 67–71 (1987). · Zbl 0633.46051
[109] B. E. Johnson, ”Approximately multiplicative maps between Banach algebras,” J. London Math. Soc. (2), 37, No. 2, 294–316 (1988). · Zbl 0652.46031
[110] B. E. Johnson, ”Derivations from L 1(G) into L 1(G) and L (G),” in: Harmonic Analysis, Proc. Int. Symp., Luxembourg, 1987, Lect. Notes Math., Vol. 1359, Springer, Berlin (1988), pp. 191–198.
[111] B. E. Johnson, ”Perturbations of multiplication and homomorphisms,” in: Deformation Theory of Algebras and Structures and Applications, NATO Adv. Study Inst., Castelvecchio–Pascoli/Italy, 1986, NATO ASI Ser., Ser. C, Math. Phys. Sci., Vol. 247, Kluwer Academic, Dordrecht (1988), pp. 565–579.
[112] B. E. Johnson, ”Near inclusions for subhomogeneous C* algebras,” Proc. London Math. Soc. (3), 68, No. 2, 399–422 (1994). · Zbl 0803.46067
[113] B. E. Johnson, ”Non-amenability of the Fourier algebra of a compact group,” J. London Math. Soc. (2), 50, No. 2, 361–374 (1994). · Zbl 0829.43004
[114] B. E. Johnson, ”Symmetric amenability and the nonexistence of Lie and Jordan derivations,” Math. Proc. Cambridge Philos. Soc., 120, No. 3, 455–473 (1996). · Zbl 0888.46024
[115] B. E. Johnson, ”Local derivations on C*-algebras are derivations,” Trans. Amer. Math. Soc., 353, No. 1, 313–325 (2001). · Zbl 0971.46043
[116] B. E. Johnson, ”The derivation problem for group algebras of connected locally compact groups,” J. London Math. Soc. (2), 63, No. 2, 441–452 (2001). · Zbl 1012.43001
[117] G. G. Kasparov, ”The operator K-functor and extensions of C*-algebras,” Math. USSR Izv., 16, No. 3, 513–572 (1981). · Zbl 0464.46054
[118] D. Kazhdan, ”On {\(\epsilon\)}-representations,” Israel J. Math., 43, No. 4, 315–323 (1982). · Zbl 0518.22008
[119] D. Kotschick, ”What is... a quasi-morphism?” Notices Amer. Math. Soc., 51, No. 2, 208–209 (2004). · Zbl 1064.20033
[120] R. A. Kunze and E. M. Stein, ”Uniformly bounded representations and harmonic analysis on the 2 {\(\times\)} 2 real unimodular group,” Amer. J. Math., 82, No. 1, 1–62 (1960). · Zbl 0156.37104
[121] N. P. Landsman, ”Strict deformation quantization of a particle in external gravitational and Yang–Mills fields,” J. Geom. Phys., 12, No. 2, 93–132 (1993). · Zbl 0789.58081
[122] A. T.-M. Lau, ”Amenability of semigroups,” in: The Analytical and Topological Theory of Semigroups, De Gruyter Exp. Math., Vol. 1, Walter de Gruyter, Berlin (1990), pp. 313–334.
[123] J. W. Lawrence, ”The stability of multiplicative semigroup homomorphisms to real normed algebras,” Aequationes Math., 28, No. 1-2, 94–101 (1985). · Zbl 0594.46047
[124] H. Lin, ”Almost multiplicative morphisms and some applications,” J. Operator Theory, 37, No. 1, 121–154 (1997). · Zbl 0869.46032
[125] H. Lin, ”When almost multiplicative morphisms are close to homomorphisms,” Trans. Amer. Math. Soc., 351, No. 12, 5027–5049 (1999). · Zbl 0945.46039
[126] H. Lin and N. C. Phillips, ”Almost multiplicative morphisms and the Cuntz algebra \(\mathcal{O}_2 \) ,” Internat. J. Math., 6, No. 4, 625–643 (1995). · Zbl 0838.46048
[127] G. G. Lorentz, ”A contribution to the theory of divergent sequences,” Acta Math., 80, 167–190 (1948). · Zbl 0031.29501
[128] T. A. Loring, ”Almost multiplicative maps between C* algebras,” in: S. Doplicher, ed., Operator Algebras and Quantum Field Theory, Proc. Conf. Dedicated to Daniel Kastler in Celebration of his 70th Birthday, Accademia Nazionale dei Lincei, Roma, Italy, July 1–6, 1996, Internat. Press, Cambridge, MA (1997), pp. 111–122. · Zbl 0906.46046
[129] T. A. Loring and G. K. Pedersen, ”Corona extendibility and asymptotic multiplicativity,” K-Theory, 11, No. 1, 83–102 (1997). · Zbl 0867.46047
[130] N. Louvet, ”A propos d’un théorème de Vershik et Karpushev,” Enseign. Math. (2), 47, No. 3-4, 287–314 (2001). · Zbl 1004.22001
[131] R. J. Loy, C. J. Read, V. Runde, and G. A. Willis, ”Amenable and weakly amenable Banach algebras with compact multiplication,” J. Funct. Anal., 171, No. 1, 78–114 (2000). · Zbl 0946.46041
[132] D. Ma, ”Upper semicontinuity of isotropy and automorphism groups,” Math. Ann., 292, No. 3, 533–545 (1992). · Zbl 0738.32019
[133] G. W. Mackey, ”Borel structure in groups and their duals,” Trans. Amer. Math. Soc., 85, 134–165 (1957). · Zbl 0082.11201
[134] J. F. Manning, ”Geometry of pseudocharacters,” Geom. Topol., 9, 1147–1185 (2005). · Zbl 1083.20038
[135] V. M. Manuilov, ”Almost representations and asymptotic representations of discrete groups,” Math. USSR Izv., 63, No. 5, 995–1014 (1999). · Zbl 0961.22008
[136] V. M. Manuilov, ”On almost representations of the groups {\(\pi\)} {\(\times\)} Z,” Proc. Steklov Inst. Math., No. 2 (225), 243–249 (1999).
[137] V. M. Manuilov, ”Almost commutativity implies asymptotic commutativity,” in: A. Gheondea, ed., Operator Theoretical Methods, Proc. 17th Int. Conf. on Operator Theory, Timi\c{}soara, Romania, June 23–26, 1998, Theta Foundation, Bucharest (2000), pp. 257–268. · Zbl 1020.47025
[138] V. M. Manuilov, ”On C*-algebras associated with asymptotic homomorphisms,” Math. Notes, 68, No. 3–4, 326–332 (2000). · Zbl 0980.46041
[139] V. M. Manuilov and A. S. Mishchenko, ”Asymptotic and Fredholm representations of discrete groups,” Sb. Math., 189, No. 10, 1485–1504 (1998). · Zbl 0932.46067
[140] V. M. Manuilov and A. S. Mishchenko, ”Almost, asymptotic and Fredholm representations of discrete groups,” Acta Appl. Math., 68, 159–210 (2001). · Zbl 1012.46061
[141] V. M. Manuilov and K. Thomsen, ”Quasidiagonal extensions and sequentially trivial asymptotic homomorphisms,” Adv. Math., 154, 258–279 (2000). · Zbl 0974.46052
[142] V. M. Manuilov and K. Thomsen, ”Asymptotically split extensions and E-theory,” St. Petersburg Math. J., 12, No. 5, 819–830 (2001). · Zbl 1012.46060
[143] V. M. Manuilov and K. Thomsen, ”The Connes–Higson map is an isomorphism,” Russ. Math. Surv., 56, No. 4, 756–757 (2001). · Zbl 1032.46090
[144] V. M. Manuilov and K. Thomsen, ”E-theory is a special case of KK-theory,” Proc. London Math. Soc. (3), 88, No. 2, 455–478 (2004). · Zbl 1045.19001
[145] V. M. Manuilov and K. Thomsen, ”Semi-invertible extensions and asymptotic homomorphisms,” K-Theory, 32, No. 2, 101–138 (2004). · Zbl 1074.46037
[146] V. M. Manuilov and K. Thomsen, ”The Connes–Higson construction is an isomorphism,” J. Funct. Anal., 213, No. 1, 154–175 (2004). · Zbl 1065.46051
[147] V. M. Manuilov and K. Thomsen, ”Translation invariant asymptotic homomorphisms and extensions of C*-algebras,” Funct. Anal. Appl., 39, No. 3, 236–239 (2005). · Zbl 1122.46052
[148] D. McDuff, ”A survey of the topological properties of symplectomorphism groups,” in: Topology, Geometry and Quantum Field Theory, London Math. Soc. Lect. Note Ser., Vol. 308, Cambridge Univ. Press, Cambridge (2004), pp. 173–193. · Zbl 1102.57013
[149] M. Megrelishvili, ”Generalized Heisenberg groups and Shtern’s question,” Georgian Math. J., 11, No. 4, 775–782 (2004). · Zbl 1062.22002
[150] A. S. Mishchenko, ”On Fredholm representations of discrete groups,” Funct. Anal. Appl., 9, No. 2, 121–125 (1975). · Zbl 0318.57050
[151] A. S. Mishchenko and N. Mohammad, ”Asymptotic representation of discrete groups,” in: Lie Groups and Lie Algebras, Math. Appl., Vol. 433, Kluwer Academic, Dordrecht (1998), pp. 299–312. · Zbl 0909.22008
[152] N. Monod, Continuous Bounded Cohomology of Locally Compact Groups, Lect. Notes Math., Vol. 1758, Springer, Berlin (2001). · Zbl 0967.22006
[153] N. Monod and B. Remy, Boundedly generated groups with pseudocharacter(s), arXiv:math.GR/0310065, pp. 21–23.
[154] D. Montgomery and L. Zippin, ”A theorem on Lie groups,” Bull. Amer. Math. Soc., 48, 448–452 (1942). · Zbl 0063.04079
[155] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience Publishers, New York (1955). · Zbl 0068.01904
[156] C. C. Moore, ”Group extensions and cohomology for locally compact groups. III,” Trans. Amer. Math. Soc., 221, No. 1, 1–33 (1976). · Zbl 0366.22005
[157] R. T. Moore, Measurable, Continuous and Smooth Vectors for Semi-Groups and Group Representations, Mem. Amer. Math. Soc., Vol. 78, Amer. Math. Soc., Providence (1968).
[158] M. A. Naimark and A. I. Štern [Shtern], Theory of Group Representations, Springer, Berlin (1982).
[159] K.-H. Neeb, ”On a theorem of S. Banach,” J. Lie Theory, 7, No. 2, 293–300 (1997). · Zbl 0904.22002
[160] K.-H. Neeb and D. Pickrell, ”Supplements to the papers entitled: ’On a theorem of S. Banach’ and ’The separable representations of U(H)’,” J. Lie Theory, 10, No. 1, 107–109 (2000). · Zbl 0942.22004
[161] J. von Neumann, ”Approximative properties of matrices of high finite order,” Portugal. Math., 3, 1–62 (1942). · Zbl 0026.23302
[162] N. Nikolov and D. Segal, ”Finite index subgroups in profinite groups,” C. R., Math., Acad. Sci. Paris, 337, No. 5, 303–308 (2003). · Zbl 1033.20029
[163] N. Nikolov and D. Segal, ”On finitely generated profinite groups. I: Strong completeness and uniform bounds,” Ann. Math., 165, 171–238 (2007). · Zbl 1126.20018
[164] N. Nikolov and D. Segal, ”On finitely generated profinite groups. II: Products in quasisimple groups,” Ann. Math., 165, 239–273 (2007). · Zbl 05157394
[165] A. L. T. Paterson, Amenability, Amer. Math. Soc., Providence (1988).
[166] V. G. Pestov, ”Amenable representations and dynamics of the unit sphere in an infinite-dimensional Hilbert space,” Geom. Funct. Anal., 10, No. 5, 1171–1201 (2000). · Zbl 0976.43001
[167] J.-C. Picaud, ”Cohomologie bornée des surfaces et courants géodésiques,” Bull. Soc. Math. France, 125, No. 1, 115–142 (1997).
[168] D. R. Pitts, ”Perturbations of certain reflexive algebras,” Pacific J. Math., 165, No. 1, 161–180 (1994). · Zbl 0808.47033
[169] H. Poincaré, ”Mémoire sur les courbes définies par une équation différentielle,” J. de Mathématiques, 8, 251–296 (1882); H. Poincaré, OEuvres, I, Gauthier-Villars, Paris (1928). · JFM 14.0666.01
[170] L. Polterovich and Z. Rudnick, ”Stable mixing for cat maps and quasi-morphisms of the modular group,” Ergodic Theory Dynam. Syst., 24, No. 2, 609–619 (2004). · Zbl 1071.37019
[171] P. Py, Quasi-Morphismes et Invariant de Calabi, arXiv:math.SG/0506096 (2005).
[172] H. Rademacher, ”Zur Theorie der Modulfunktionen,” J. Reine Angew. Math., 167, 312–336 (1932). · Zbl 0003.21501
[173] I. Raeburn and J. L. Taylor, ”Hochschild cohomology and perturbations of Banach algebras,” J. Funct. Anal., 25, No. 3, 258–266 (1977). · Zbl 0349.46043
[174] M. Rajagopalan, ”Characters of locally compact Abelian groups,” Math. Z., 86, 268–272 (1964). · Zbl 0199.06601
[175] C. J. Read, ”Commutative, radical amenable Banach algebras,” Studia Math., 140, No. 3, 199–212 (2000). · Zbl 0972.46031
[176] H. Rindler, ”Unitary representations and compact groups,” Arch. Math. (Basel), 58, No. 5, 492–499 (1992). · Zbl 0738.43009
[177] P. J. Sally, Jr., Analytic Continuation of the Irreducible Unitary Representations of the Universal Covering Group of SL(2, \(\mathbb{R}\)), Mem. Amer. Math. Soc., Vol. 69, Amer. Math. Soc., Providence (1967). · Zbl 0157.20702
[178] A. Sambusetti, ”Minimal entropy and simplicial volume,” Manuscripta Math., 99, No. 4, 541–560 (1999). · Zbl 0982.53033
[179] Z. Sasvari, Positive Definite and Definitizable Functions, Akademie, Berlin (1994).
[180] H. H. Schaefer, Topological Vector Spaces, Collier–Macmillan, London (1966). · Zbl 0141.30503
[181] G. Segal, ’Cohomology of topological groups,” in: Symposia Mathematica, Roma, Vol. IV, Teoria Numeri, Dic. 1968, e Algebra, Marzo 1969, Academic Press, London (1970), pp. 377–387.
[182] P. Šemrl, ”Hyers–Ulam stability of isometries on Banach spaces,” Aequationes Math., 58, 157–162 (1999). · Zbl 0944.46005
[183] P. Šemrl, ”Almost multiplicative functions and almost linear multiplicative functionals,” Aequationes Math., 63, 180–192 (2002). · Zbl 1007.39024
[184] Y. Shalom, ”Bounded generation and Kazhdan’s property (T),” Inst. Hautes Études Sci. Publ. Math. (1999), 90, 145–168 (2001). · Zbl 0980.22017
[185] E. T. Shavgulidze, ”Some properties of quasi-invariant measures on groups of diffeomorphisms of the circle,” Russ. J. Math. Phys., 7, No. 4, 464–472 (2000). · Zbl 1072.37503
[186] E. T. Shavgulidze, ”Properties of the convolution operation for quasi-invariant measures on groups of diffeomorphisms of a circle,” Russ. J. Math. Phys., 8, No. 4, 495–498 (2001). · Zbl 1186.58010
[187] A. I. Shtern, ”The rigidity of positive characters,” Usp. Mat. Nauk, 35, No. 5, 218 (1980).
[188] A. I. Shtern, ”On stability of homomorphisms in the group R*,” Moscow Univ. Math. Bull., 37, No. 3, 33–36 (1982). · Zbl 0497.39004
[189] A. I. Shtern, ”The stability of representations and pseudocharacters,” in: Lomonosov Conference, Moscow State Univ., Moscow (1983). · Zbl 1168.37305
[190] A. I. Shtern, ”A pseudocharacter that is determined by the Rademacher symbol,” Russ. Math. Surv., 45, No. 3, 224–226 (1990). · Zbl 0724.11024
[191] A. I. Shtern, ”Quasirepresentations and pseudorepresentations,” Funct. Anal. Appl., 25, No. 2, 140–143 (1991). · Zbl 0737.22003
[192] A. I. Shtern, ”On operators in Fréchet spaces that are similar to isometries,” Moscow Univ. Math. Bull., 46, No. 4, 47–48 (1991). · Zbl 0802.46002
[193] A. I. Shtern, ”Almost convergence and its applications to the Fourier–Stieltjes localization,” Russ. J. Math. Phys., 1, No. 1, 115–125 (1993). · Zbl 0872.43002
[194] A. I. Shtern, ”Characterizations of amenable groups in the class of connected locally compact groups,” Russ. Math. Surv., 49, No. 2, 174–175 (1994).
[195] A. I. Shtern, ”Quasi-symmetry. I,” Russ. J. Math. Phys., 2, No. 3, 353–382 (1994). · Zbl 0907.22007
[196] A. I. Shtern, Remarks on Pseudocharacters and the Real Continuous Bounded Cohomology of Connected Locally Compact Groups, Sfb 288 Preprint No. 289 (1997).
[197] A. I. Shtern, ”Almost representations and quasi-symmetry,” in: B. P. Komrakov, I. S. Krasil’shchik, G. L. Litvinov, and A. B. Sossinsky, eds., Lie Groups and Lie Algebras. Their Representations, Generalizations and Applications, Math. Its Appl., Vol. 433, Kluwer Academic, Dordrecht (1998), pp. 337–358. · Zbl 0896.22002
[198] A. I. Shtern, ”Quasi-symmetry and amenability,” in: Abstracts of Reports, ICM-98, Vol. II, Berlin (1998), p. 138. · Zbl 0896.22002
[199] A. I. Shtern, ”Triviality and continuity of pseudocharacters and pseudorepresentations,” Russ. J. Math. Phys., 5, No. 1, 135–138 (1998). · Zbl 0945.43002
[200] A. I. Shtern, ”Rigidity and approximation of quasi-representations of amenable groups,” Math. Notes, 65, No. 6, 760–769 (1999). · Zbl 0952.43002
[201] A. I. Shtern, ”A criterion for the second real continuous bounded cohomology of a locally compact group to be finite-dimensional,” Acta Appl. Math., 68, No. 1–3, 105–121 (2001). · Zbl 0997.22005
[202] A. I. Shtern, ”Bounded continuous real 2-cocycles on simply connected simple Lie groups and their applications,” Russ. J. Math. Phys., 8, No. 1, 122–133 (2001). · Zbl 1082.22500
[203] A. I. Shtern, ”Remarks on pseudocharacters and the real continuous bounded cohomology of connected locally compact groups,” Ann. Global Anal. Geom., 20, No. 3, 199–221 (2001). · Zbl 0990.22002
[204] A. I. Shtern, ”Structural properties and bounded real continuous 2-cohomology of locally compact groups,” Funct. Anal. Appl., 35, No. 4, 294–304 (2001). · Zbl 0994.22010
[205] A. I. Shtern, ”Continuity of Banach representations in terms of point variations,” Russ. J. Math. Phys., 9, No. 2, 250–252 (2002). · Zbl 1104.22300
[206] A. I. Shtern, ”Criteria for weak and strong continuity of representations of topological groups in Banach spaces,” Sb. Math., 193, No. 9, 1381–1396 (2002). · Zbl 1044.22003
[207] A. I. Shtern, ”Continuity criteria for finite-dimensional representations of compact connected groups,” Adv. Stud. Contemp. Math. (Kyungshang), 6, No. 2, 141–156 (2003). · Zbl 1032.22001
[208] A. I. Shtern, ”Continuity criteria for finite-dimensional representations of groups,” in: Functional Spaces. Differential Operators. Problems of Mathematical Education [in Russian], Nauka, Moscow (2003), pp. 122–124.
[209] A. I. Shtern, ”Deformation of irreducible unitary representations of a discrete series of Hermitian symmetric simple Lie groups in the class of pure pseudo-representations,” Math. Notes, 73, No. 3–4, 452–454 (2003). · Zbl 1052.22010
[210] A. I. Shtern, ”Values of invariant means, left averaging, and criteria for a locally compact group to be amenable as discrete group,” Russ. J. Math. Phys., 10, No. 2, 185–198 (2003). · Zbl 1039.43003
[211] A. I. Shtern, ”Continuity conditions for finite-dimensional representations of some compact totally disconnected groups,” Adv. Stud. Contemp. Math. (Kyungshang), 8, No. 1, 13–22 (2004). · Zbl 1052.22002
[212] A. I. Shtern, ”Continuity conditions for finite-dimensional representations of some compact totally disconnected groups,” Adv. Stud. Contemp. Math. (Kyungshang), 8, No. 1, 13–22 (2004). · Zbl 1052.22002
[213] A. I. Shtern, ”Criteria for the continuity of finite-dimensional representations of connected locally compact groups,” Sb. Math., 195, No. 9, 1377–1391 (2004). · Zbl 1075.22002
[214] A. I. Shtern, ”Deformations of irreducible unitary representations of a discrete series of Hermitian symmetric simple Lie groups in the class of pure pseudo-representations,” J. Math. Sci., 123, No. 4, 4324–4339 (2004). · Zbl 1071.22015
[215] A. I. Shtern, ”Projective irreducible unitary representations of Hermitian symmetric simple Lie groups are generated by pure pseudorepresentations,” Adv. Stud. Contemp. Math. (Kyungshang), 9, No. 1, 1–6 (2004). · Zbl 1060.22013
[216] A. I. Shtern, ”Almost periodic functions and representations in locally convex spaces,” Russ. Math. Surv., 60, No. 3, 489–557 (2005). · Zbl 1119.43005
[217] A. I. Shtern, ”Projective representations and pure pseudorepresentations of Hermitian symmetric simple Lie groups,” Math. Notes, 78, No. 1-2, 128–133 (2005). · Zbl 1102.22011
[218] A. I. Shtern, ”Van der Waerden continuity theorem for arbitrary semisimple Lie groups,” Russ. J. Math. Phys., 13, No. 2, 210–223 (2006). · Zbl 1128.22006
[219] A. I. Shtern, ”Van der Waerden continuity theorem for the Poincaré group and for some other group extensions,” Adv. Theor. Appl. Math., 1, No. 1, 79–90 (2006). · Zbl 1151.22015
[220] A. I. Shtern, ”Van der Waerden’s continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko’s conjecture,” Adv. Stud. Contemp. Math. (Kyungshang), 13, No. 2, 143–158 (2006). · Zbl 1111.22007
[221] A. I. Shtern, ”Weak and strong continuity of representations of topologically pseudocomplete groups in locally convex spaces,” Sb. Math., 197, No. 3, 453–473 (2006). · Zbl 1137.22002
[222] A. I. Shtern, ”Automatic continuity of pseudocharacters on Hermitian symmetric semisimple Lie groups,” Adv. Stud. Contemp. Math. (Kyungshang), 12, No. 1, 1–8 (2007). · Zbl 1084.22012
[223] A. I. Shtern, ”Kazhdan–Mil’man problem for semisimple compact Lie groups,” Russ. Math. Surv., 62, No. 1, 123–190 (2007). · Zbl 1179.22005
[224] A. I. Shtern, ”Stability of the van der Waerden theorem on the continuity of homomorphisms of compact semisimple Lie groups,” Appl. Math. Comput., 187, No. 1, 455–465 (2007). · Zbl 1122.22001
[225] A. I. Shtern, ”A version of the van der Waerden theorem and the proof of the Mishchenko conjecture for homomorphisms of locally compact groups” (to appear).
[226] H. Shulman and D. Tischler, ”Leaf invariants for foliations and the van Est isomorphism,” J. Differential Geom., 11, 535–546 (1976). · Zbl 0361.57022
[227] S. J. Sidney, ”Are all uniform algebras AMNM?” Bull. London Math. Soc., 29, No. 3, 327–330 (1997). · Zbl 0865.46035
[228] A. M. Sinclair and R. R. Smith, Hochschild Cohomology of von Neumann Algebras, London Math. Soc. Lect. Note Ser., Vol. 203, Cambridge Univ. Press, Cambridge (1995). · Zbl 0826.46050
[229] N. Spronk, ”Operator weak amenability of the Fourier algebra,” Proc. Amer. Math. Soc., 130, No. 12, 3609–3617 (2002). · Zbl 1006.46040
[230] M. Stroppel, ”Lie theory for non-Lie groups,” J. Lie Theory, 4, No. 2, 257–284 (1994). · Zbl 0834.22009
[231] M. Takesaki, Theory of Operator Algebras. I, Springer, New York (1979). · Zbl 0436.46043
[232] S. Teleman, ”Sur la réprésentation lineaire des groupes topologiques,” Ann. Sci. École Norm. Sup. (3), 74, 319–339 (1957). · Zbl 0084.03106
[233] K. Thomsen, ”Nonstable K-theory for operator algebras,” Internat. J. Math., 4, No. 3, 245–267 (1991). · Zbl 0744.46069
[234] K. Thomsen, ”Asymptotic homomorphisms and equivariant KK-theory,” J. Funct. Anal., 163, No. 2, 324–343 (1999). · Zbl 0929.46059
[235] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York (1960).
[236] V. S. Varadarajan, Lie groups, Lie Algebras, and Their Representations, Prentice Hall, Englewood Cliffs (1974) · Zbl 0371.22001
[237] A. M. Vershik, ”Commentaries to the Russian translation,” in: J. von Neumann, Selected Works on Functional Analysis, Vol. 1 [in Russian], Nauka, Moscow (1987), pp. 372–374.
[238] A. M. Vershik and S. I. Karpushev, ”Cohomology of groups in unitary representations, the neighborhood of the identity, and conditionally positive definite functions,” Math. USSR Sb., 47, No. 2, 513–526 (1984). · Zbl 0528.43005
[239] B. L. van der Waerden, ”Stetigkeitssätze für halbeinfache Liesche Gruppen,” Math. Z., 36, 780–786 (1933). · Zbl 0006.39205
[240] G. Warner, Harmonic Analysis on Semi-Simple Lie Groups, Vols. I, II, Springer, New York (1972). · Zbl 0265.22021
[241] M. C. White, ”Characters on weighted amenable groups,” Bull. London Math. Soc., 23, No. 4, 375–380 (1991). · Zbl 0748.43002
[242] G. A. Willis, ”The continuity of derivations from group algebras: Factorizable and connected groups,” J. Aust. Math. Soc. Ser. A, 52, 185–204 (1992). · Zbl 0763.46045
[243] G. V. Wood, ”Small isomorphisms between group algebras,” Glasgow Math. J., 33, No. 1, 21–28 (1991). · Zbl 0724.43004
[244] G. Yu, ”The Novikov conjecture for groups with finite asymptotic dimension,” Ann. Math. (2), 147, No. 2, 325–355 (1998). · Zbl 0911.19001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.