×

Non-self-adjoint operator algebras in Hilbert space. (English) Zbl 0351.46043


MSC:

47L30 Abstract operator algebras on Hilbert spaces
47A15 Invariant subspaces of linear operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] N. Aronzajn and C. Smith, ?Invariant subspaces of completely continuous operators,? Matematika,2, No. 1, 97?102 (1958).
[2] M. S. Brodskii, ?A problem of I. M. Gel’fand,? Usp. Matem. Nauk,12, No. 2, 129?132 (1957).
[3] M. S. Brodskii, ?Triangular and Jordan Representations of Linear Operators [in Russian], Nauka, Moscow (1969).
[4] M. S. Brodskii, I. Ts. Gokhbert, M. G. Krein, and V. I. Mal’tsev, Trans. All-Union Mathematical Congress, 1961 [in Russian], Vol. 2, Nauka, Leningrad (1964), pp. 261?271.
[5] T. Gamelin, Uniform Algebras [Russian translation], Mir, Moscow (1973). · Zbl 0325.30035
[6] K. Hoffman, Banach Spaces of Analytic Functions [Russian translation], Izd-vo In. Lit., Moscow (1963). · Zbl 0117.34002
[7] I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Non-Self-Adjoint Operators in Hilbert Spaces [in Russian], Nauka, Moscow (1965).
[8] I. Ts. Gokhberg and M. G. Krein, Theory of Volterra Operators in Hilbert Space and Applications [in Russian], Nauka, Moscow (1967). · Zbl 0161.11601
[9] N. Dunford and J. Schwartz, Linear Operators. II [Russian translation], Mir, Moscow (1966).
[10] R. S. Ismagilov, ?Rings of operators in a space with indefinite metric,? Dokl. Akad. Nauk SSSR,171, No. 2, 269?271 (1966). · Zbl 0162.18801
[11] G. É. Kiselevskii, ?Invariant subspaces of dissipative Volterra operators with imaginary nuclear components,? Izv. Akad. Nauk SSSR. Ser. Matem.,32, No. 1, 3?23 (1968).
[12] É. V. Kissin, ?C*-algebras generated by dynamic systems and weighted shifts,? Dokl. Akad. Nauk SSSR,216, No. 6, 1215?1218 (1974). · Zbl 0312.46074
[13] B. I. Korenblyum, ?Invariant subspaces of shift operators in a Hilbert weight space,? Matem. Sb.,89, No. 1, 110?137 (1972). · Zbl 0229.30034
[14] M. G. Krein, ?Positively additive functionals in linear normed spaces,? Zap. Naukove Doslid. Inst. Matem. i Mekh. KhDU i Kharkov Matem. Tov.,14, 227?237 (1937).
[15] V. I. Liberzon and V. S. Shul’man, ?Nondegenerate operator algebras in IIk spaces with indefinite metric,? Izv. Akad. Nauk SSSR. Ser. Matem.,37, No. 3, 533?538 (1973).
[16] V. I. Liberzon and V. S. Shul’man, ?Operator-irreducible symmetric operator algebras in the II1 Pontryagin space,? Izv. Akad. Nauk SSSR. Ser. Matem.,35, No. 5, 1159?1170 (1971).
[17] M. S. Lifshits, Operators, Oscillations, Waves. Open Systems [in Russian], Nauka, Moscow (1966).
[18] A. I. Loginov, ?Commutative symmetric Banach operator algebras in the II1 Pontryagin space,? Dokl. Akad. Nauk SSSR,179, No. 6, 1276?1278 (1968).
[19] A. I. Loginov, ?Complete commutative symmetric operator algebras in the II1 Pontryagin space,? Matem. Sb.,84, No. 4, 575?582 (1971). · Zbl 0231.46104
[20] A. I. Loginov and V. S. Shul’man, ?Sarason’s theorem and the Radjavi-Rosenthal hypothesis,? Dokl. Akad. Nauk SSSR,205, No. 2, 284?285 (1972). · Zbl 0265.46067
[21] A. I. Loginov and V. S. Shul’man, ?Hereditary and intermediate reflexivity of W*-algebras,? Dokl. Akad. Nauk SSSR,212, No. 4, 34?36 (1973). · Zbl 0312.46082
[22] A. I. Loginov and V. S. Shul’man, ?Reductive operator algebras and the invariant subspace problem,? Dokl. Akad. Nauk SSSR,216, No. 1, 36?38 (1974).
[23] V. I. Lomonosov, ?Invariant subspaces of a family of operators that commute with a completely continuous operator,? Funkts. Anal. i Ego Prilozh.,7, No. 3, 55?56 (1973).
[24] V. I. Matsaev, ?A class of completely continuous operators,? Dokl. Akad. Nauk SSSR,138, No. 3, 548?551 (1961).
[25] M. A. Naimark, Linear Representations of the Lorentz Group [in Russian], Fizmatgiz, Moscow (1958), 376 pp.
[26] M. A. Naimark, Normed Rings [in Russian], Nauka, Moscow (1968).
[27] M. A. Naimark, ?Commuting unitary operators in the ?? space,? Dokl. Akad. Nauk SSSR,149, No. 6, 1261?1263 (1963).
[28] M. A. Naimark, ?Commutative operator algebras in the II1 space,? Dokl. Akad. Nauk SSSR,156, No. 4, 734?737 (1964).
[29] M. A. Naimark, ?Commutative operator algebras in the II1 space,? Rev. Roum. Math. Pures Appl.,9, No. 6, 499?528 (1964).
[30] M. A. Naimark, ?Commutative operator algebras in the IIk space,? Dokl. Akad. Nauk SSSR,161, No. 4, 767?770 (1965).
[31] M. A. Naimark, ?Structure of unitary representations of locally bicompact groups in the II1 space,? Izv. Akad. Nauk SSSR. Ser. Matem.,29, No. 3, 689?770 (1965).
[32] M. A. Naimark, ?Structure of unitary representations of locally bicompact groups and symmetric representations of algebras in the Pontryagin IIk space,? Izv. Akad. Nauk SSSR. Set. Matem.,30, No. 5, 1111?1132 (1966).
[33] M. A. Naimark and R. S. Ismagilov, ?Representations of groups and algebras in spaces with indefinite metric,? in: Progress in Science. Mathematical Analysis. 1968 [in Russian], VINITI Akad. Nauk SSSR, Moscow (1969), pp. 73?105.
[34] N. K. Nikol’skii, ?Invariant subspaces of certain completely continuous operators,? Vestn. Leningr. Univ., No. 7, 68?77 (1965).
[35] N. K. Nikol’skii, ?Invariant subspaces of unitary operators,? Vestn. Leningr. Univ., No. 19, 36?43 (1966).
[36] N. K. Nikol’skii, ?Unicellularity and nonunicellularity of weighted shift operators,? Dokl. Akad. Nauk SSSR,172, No. 2, 287?290 (1967). · Zbl 0157.21202
[37] N. K. Nikol’skii, ?Invariant subspaces of weighted shift operators,? Matem. Sb.,74, No. 2, 171?190 (1967).
[38] N. K. Nikol’skii, ?Basicity and unicellularity of weighted shift operators,? Funkts. Anal. i Ego Prilozh.,2, No. 2, 95?96 (1968).
[39] N. K. Nikol’skii, ?Nonstandard ideals, unicellularity, and algebras related to the shift operator,? Zap. Nauch. Semin. Leningr. Otd. Matem. Inst. Akad. Nauk SSSR,19, 156?195 (1970).
[40] L. S. Pontryagin, ?Hermitian operators in a space with indefinite metric,? Izv. Akad. Nauk SSSR. Ser. Matem.,8, No. 1, 243?280 (1944). · Zbl 0061.26004
[41] L. A. Sakhnovich, ?Reduction of Volterra operators to simplest form and inverse problems,? Izv. Akad. Nauk SSSR,21, 235?262 (1957).
[42] B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators in Hilbert Space [Russian translation], Mir, Moscow (1970), 431 pp.
[43] R. R. Phelps, Lectures on Choquet’s Theorem [Russian translation], Mir, Moscow (1968). · Zbl 0172.15603
[44] P. Halmos, Hilbert Space in Problems [Russian translation], Mir, Moscow (1970), 352 pp. · Zbl 0204.15001
[45] P. Halmos, ?Then problems in the theory of Hilbert spaces,? Matematika,15, No. 4, 28?67 (1971).
[46] P. Halmos, ?Multiplication operators in C* -algebras and reflexivity problem,? Dokl Akad. Nauk SSSR,210, No. 3, 543?544 (1973).
[47] P. Halmos, ?Reflexive operator algebras,? Matem. Sb.,87, No. 2, 92?93 (1972).
[48] P. Halmos, ?Multiplication operators in C* -algebras in reflexivity problems for algebras containing m.a.s.a.,? Funkts. Anal. i Ego Prilozh.,8, No. 1, 92?93 (1974).
[49] P. Halmos, ?Operator algebras with strictly cyclic vectors,? Matem. Zametki,16, No. 2, 253?257 (1974).
[50] P. Halmos, ?Operator algebras in a typeII1 space with indefinite metric,? Dokl. Akad. Nauk SSSR,201, No. 1, 44?47 (1971).
[51] P. Halmos, ?Symmetric Banach operator algebras in a type II1 space,? Matem. Sb.,89, No. 2, 264?279 (1972).
[52] T. Andô, ?On a pair of commutative contractions,? Acta Sci. Math.,24, Nos. 1?2, 88?90 (1963). · Zbl 0116.32403
[53] T. Andô, ?A note on invariant subspaces of a compact normal operator,? Arch. Math.,14, Nos. 4?5, 337?340 (1963). · Zbl 0125.34703 · doi:10.1007/BF01234964
[54] C. Apostol, ?Hypercommutativity and invariant subspaces,? Rev. Roum. Math. Pures Appl.,17, No. 3, 335?339 (1972). · Zbl 0239.47014
[55] C. Apoltol, ?Quasitriangularity in Hilbert space,? Indiana Univ. Math. J.,22, No. 9, 817?825 (1973). · Zbl 0254.47028 · doi:10.1512/iumj.1973.22.22069
[56] C. Apoltol, C. Foias, and L. Zsido, ?On non-quasitriangular operators,? C. R. Acad. Sci.,275, No. 10, A501-A503 (1972).
[57] C. Apostol, C. Foias, and D. Voiculescu, ?Spectral structure of nonquasitriangular operators,? C. R. Acad. Sci.,276, No. 1, A49-A51 (1973).
[58] C. Apostol, C. Foias, and D. Voisculescu, ?Some results on non-quasitriangular operators. II,? Rev. Roum. Math. Pures Appl.,18, No. 2, 159?181 (1973).
[59] C. Apostol, C. Foias, and D. Voisculescu, ?Some results on nonquasitriangular operators. III,? Rev. Roumn. Math. Pures Appl.,18, No. 3, 309?324 (1973).
[60] C. Apostol, C. Foias, and D. Voisculescu, ?Some results on nonquasitriangular operators. IV,? Rev. Roumn. Math. Pures Appl.,18, No. 4, 487?514 (1973).
[61] W. B. Arveson, ?A density theorem for operator algebras,? Duke Math. J.,34, 635?647 (1967). · Zbl 0183.42403 · doi:10.1215/S0012-7094-67-03467-9
[62] W. B. Arveson, ?An algebraic conjugacy invariant for measure preserving automorphisms,? Bull. Amer. Math. Soc.,73, No. 1, 121?125 (1967). · Zbl 0182.18202 · doi:10.1090/S0002-9904-1967-11675-6
[63] W. B. Arveson, ?Operator algebras and measure preserving automorphisms,? Acta Math.,118, Nos. 1?2, 95?109 (1967). · Zbl 0182.18201 · doi:10.1007/BF02392478
[64] W. B. Arveson, ?Analyticity in operator algebras,? Amer. J. Math.,89, No. 3, 578?642 (1967). · Zbl 0183.42501 · doi:10.2307/2373237
[65] W. B. Arveson, ?On subalgebras of C*-algebras,? Bull. Amer. Math. Soc.,75, No. 4, 790?794 (1969). · Zbl 0212.15402 · doi:10.1090/S0002-9904-1969-12293-7
[66] W. B. Arveson, ?Subalgebras of C*-algebras. I,? Acta Math.,123, Nos. 3?4, 141?224 (1969). · Zbl 0194.15701 · doi:10.1007/BF02392388
[67] W. B. Arveson, ?Subalgebras of C*-algebras. II,? Acta Math.,128, Nos. 3?4, 271?308 (1972). · Zbl 0245.46098 · doi:10.1007/BF02392166
[68] W. B. Arveson, ?Unitary invariants for compact operators,? Bull. Amer. Math. Soc.,76, No. 1, 88?91 (1970). · Zbl 0196.14304 · doi:10.1090/S0002-9904-1970-12374-6
[69] W. B. Arveson, ?Lattices of invariant subspaces,? Bull. Amer. Math. Soc.,78, No. 4, 515?519 (1972). · Zbl 0258.47005 · doi:10.1090/S0002-9904-1972-12977-X
[70] W. B. Arveson and J. Feldman, ?A note on invariant subspaces,? Mich. Math. J.,15, No. 1, 61?64 (1968). · Zbl 0167.13304 · doi:10.1307/mmj/1028999905
[71] W. B. Arveson and K. B. Josephson, ?Operator algebras and measure preserving automorphisms. II,? J. Funct. Anal.,4, No. 1, 100?134 (1969). · doi:10.1016/0022-1236(69)90025-1
[72] W. G. Bade, ?Weak and strong limits of spectral operators,? Pacif. J. Math.,4, No. 3, 393?413 (1954). · Zbl 0056.34802 · doi:10.2140/pjm.1954.4.393
[73] B. A. Barnes, ?Density theorem for algebras of operators and annihilator Banach algebras,? Mich. Math. J.,19, No. 2, 149?155 (1972). · Zbl 0233.46067 · doi:10.1307/mmj/1029000846
[74] B. A. Barnes, ?Irreducible algebras of operators which contain a minimal idempotent,? Proc. Amer. Math. Soc.,30, No. 2, 337?342 (1971). · Zbl 0226.46072
[75] H. Behncke, ?Structure of certain nonnormal operators. II,? Indiana Univ. Math. J.,22, No. 4, 301?308 (1972). · Zbl 0228.47025 · doi:10.1512/iumj.1973.22.22025
[76] C. A. Berger, ?Normal dilations,? Doctoral Dissertation, Cornell Univ. (1963), 67 pp.; Dissert. Abstrs.,24, No. 7, 2918 (1964).
[77] A. Bernstein and A. Robinson, ?Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos,? Pacif. J. Math.,16, No. 3, 421?431 (1966). · Zbl 0141.12903 · doi:10.2140/pjm.1966.16.421
[78] A. Beurling, ?On two problems concerning linear transformations in Hilbert space,? Acta Math.,81, 239?255 (1949). · Zbl 0033.37701 · doi:10.1007/BF02395019
[79] E. Bishop, ?A generalization of the Stone-Weierstrass theorem,? Pacif. J. Math.,11, No. 3, 777?783 (1961). · Zbl 0104.09002 · doi:10.2140/pjm.1961.11.777
[80] R. Bolstein, ?Strictly cyclic operators,? Duke Math. J.,40, No. 3, 683?688 (1973). · Zbl 0268.47023 · doi:10.1215/S0012-7094-73-04060-X
[81] R. Bolstein and W. Wogen, ?Subnormal operators in strictly cyclic operator algebras,? Pacif. J. Math.,49, No. 1, 7?11 (1973). · Zbl 0274.46056 · doi:10.2140/pjm.1973.49.7
[82] R. Bouldin, ?Reducing decomposition for strictly cyclic operators,? Proc. Amer. Math. Soc.,40, No. 2, 477?481 (1973). · Zbl 0267.47015 · doi:10.1090/S0002-9939-1973-0320777-7
[83] J. Bram, ?Subnormal operators,? Duke Math. J.,22, No. 1, 75?94 (1955). · Zbl 0064.11603 · doi:10.1215/S0012-7094-55-02207-9
[84] S. Brehmer, ?Uber vertauschbare Kontractionen des Hilbertschen Raumes,? Acta Sci. Math.,22, Nos. 1?2, 106?111 (1961). · Zbl 0097.31701
[85] J. E. Brennan, ?Point evaluation and invariant subspaces,? Indiana Univ. Math. J.,20, No. 10, 879?881 (1971). · Zbl 0216.41703 · doi:10.1512/iumj.1971.20.20070
[86] J. E. Brennan, ?Invariant subspaces and rational approximation,? J. Funct. Anal.,7, No. 2, 285?310 (1971). · Zbl 0214.37604 · doi:10.1016/0022-1236(71)90036-X
[87] L. Brickman and P. A. Fillmore, ?The invariant subspace lattice of a linear transformation,? Can. J. Math.,19, No. 4, 810?822 (1967). · Zbl 0153.04801 · doi:10.4153/CJM-1967-075-4
[88] L. Brown, A. Shields, and K. Zeller, ?On absolutely convergent exponential sums,? Trans. Amer. Math. Soc.,96, No. 1, 162?183 (1960). · Zbl 0096.05103 · doi:10.1090/S0002-9947-1960-0142763-8
[89] Doan Khanh Bui, ?Invariant subspaces of normal operators,? Bull. Sci. Math.,93, Nos. 3?4, 175?180 (1969?1970). · Zbl 0748.65091
[90] J. W. Bunce and J. A. Deddens, ?Irreducible representation of the C*-algebras generated by an n-normal operator,? Trans. Amer. Math. Soc.,171, Sept., 301?307 (1973).
[91] J. W. Bunce and J. A. Deddens, ?C*-algebras generated by weighted shifts,? Indiana Univ. Math. J.,23, No. 3, 257?271 (1973). · doi:10.1512/iumj.1974.23.23022
[92] M.-D. Choi, ?Positive linear maps on C*-algebras,? Can. J. Math.,24, No. 3, 520?529 (1972). · Zbl 0235.46090 · doi:10.4153/CJM-1972-044-5
[93] L. A. Coburn, ?The C*-aigebra generated by an isometry,? Bull. Amer. Math. Soc.,73, No. 5, 722?726 (1967). · Zbl 0153.16603 · doi:10.1090/S0002-9904-1967-11845-7
[94] L. A. Coburn, ?The C*-algebra generated by an isometry. II,? Trans. Amer. Math. Soc.,137, 211?217 (1969). · Zbl 0186.19704
[95] J. B. Conway, ?On algebras of operators with totally ordered lattices of invariant subspaces,? Proc. Amer. Math. Soc.,28, No. 1, 163?169 (1971). · Zbl 0214.38404 · doi:10.1090/S0002-9939-1971-0283607-6
[96] T. Crimmins and P. Rosenthal, ?On decomposition of invariant subspacss,? Bull. Amer. Math. Soc.,73, No. 1 (1967). · Zbl 0147.34401
[97] C. Davis, H. Radjavl and P. Rosenthal, ?On operator algebras and invariant subspaces,? Can. J. Math.,21, No. 5, 1178?1181 (1969). · Zbl 0186.45301 · doi:10.4153/CJM-1969-129-9
[98] D. Deckard, R. G. Douglas and C. Pearcy, ?On invariant subspaces of quasi-triangular operators,? Amer. J. Math.,51, No. 3, 637?647 (1969). · Zbl 0186.19206 · doi:10.2307/2373343
[99] J. A. Deddens, ?Reflexive operators,? Indiana Univ. Math. J.,20, No. 10, 887?889 (1971). · Zbl 0197.10004 · doi:10.1512/iumj.1971.20.20072
[100] J. A. Deddens, ?Every isometry is reflexive,? Proc. Amer. Math. Soc.,28, No. 2, 509?512 (1971). · Zbl 0213.14304 · doi:10.1090/S0002-9939-1971-0278099-7
[101] J. A. Deddens, ?Intertwining analytic Toeplitz operators,? Mich. Math. J.,18, No. 3, 243?246 (1971). · doi:10.1307/mmj/1029000685
[102] J. Dixmier, Operator Algebras in Hilbert Spaces (von Neumann Algebras), 2nd ed. rev. and suppl., Gauthier-Villars, Paris (1969), 367 pp.
[103] W. F. Donoghue, Jr., ?The lattice of invariant of a completely continuous quasi-nilpotent transformation,? Pacif. J. Math.,7, No. 2, 1031?1035 (1957). · Zbl 0078.29504 · doi:10.2140/pjm.1957.7.1031
[104] R. G. Douglas, ?On the hyperinvariant subspaces of isometries,? Math. Z.,107, No. 4, 297?300 (1968). · Zbl 0164.16403 · doi:10.1007/BF01110017
[105] R. G. Douglas, ?On the operator equations S*XT=X and related topics,? Acta Sci. Math.,30, Nos. 1?2, 19?32 (1969).
[106] R. G. Douglas, ?On the C*-algebras of a one-parameter semigroup of isometries,? Acta Math.,128, Nos. 3?4, 143?151 (1972). · Zbl 0232.46063 · doi:10.1007/BF02392163
[107] R. G. Douglas and C. Pearcy, ?On topology for invariant subspaces,? J. Funct. Anal.,2, No. 3, 323?341 (1968). · Zbl 0174.17903 · doi:10.1016/0022-1236(68)90010-4
[108] R. G. Douglas and C. Pearcy, ?A note on quasitriangular operators,? Duke Math. J.,37, No. 1, 177?188 (1970). · Zbl 0194.43901 · doi:10.1215/S0012-7094-70-03724-5
[109] R. G. Douglas and C. Pearcy, ?Hyperinvariant subspaces and transitive algebras,? Mich. Math., J.,19, No. 1, 1?12 (1972). · Zbl 0233.47005 · doi:10.1307/mmj/1029000793
[110] H. A. Dye, ?On groups of measure-preserving transformation. I,? Amer. J. Math.,81, No. 1, 119?159 (1959). · Zbl 0087.11501 · doi:10.2307/2372852
[111] J. A. Dyer, E. A. Pedersen, and P. Porcelli, ?An equivalent formulation of the invariant subspace conjecture,? Bull. Amer. Math. Soc.,78, No. 6, 1020?1023 (1972). · Zbl 0266.47007 · doi:10.1090/S0002-9904-1972-13090-8
[112] M. R. Embry, ?On invariant subspace theorem,? Proc. Amer. Math. Soc.,32, No. 1, 331?332 (1972). · Zbl 0248.47002
[113] M. R. Embry, ?Strictly cyclic operator algebras on a Banach space,? Pacif. J. Math.,45, No. 2, 443?452 (1973). · Zbl 0253.46123 · doi:10.2140/pjm.1973.45.443
[114] J. A. Erdös, ?Some results on triangular operator algebras,? Amer. J. Math.,89, No. 1, 85?93 (1967). · Zbl 0152.13204 · doi:10.2307/2373098
[115] J. M. G. Fell, ?The structure of algebras of operator fields,? Acta Math.,106, Nos. 3?4, 233?280 (1961). · Zbl 0101.09301 · doi:10.1007/BF02545788
[116] C. Foias, ?Unele aplicatii ale multimilor spectrale. I. Masura armonic?-spectral?. Studii si cerce-tari.,? Mat. Acad. RPR,10, No. 2, 365?401 (1959).
[117] C. Foias, ?Spectral maximal spaces and decomposable operators in Banach space,? Arch. Math.,14, Nos. 4?5, 341?349 (1963). · Zbl 0176.43802 · doi:10.1007/BF01234965
[118] C. Foias, ?Invariant para-closed subspaces,? Indiana Univ. Math. J.,20, No. 10, 897?900 (1971). · Zbl 0224.47002 · doi:10.1512/iumj.1971.20.20074
[119] C. Foias, ?Invariant para-closed subspaces,? Indiana Univ. Math. J.,21, No. 10, 887?906 (1972). · Zbl 0259.47005 · doi:10.1512/iumj.1972.21.21072
[120] C. Foias, ?On the scalar parts of a decomposable operator,? Rev. Roumn. Math. Pures Appl.17, No. 8, 1181?1198 (1972).
[121] C. Foias and J. P. Williams, ?Some remarks on Volterra operators,? Proc. Amer. Math. Soc.,31, No. 1, 177?184 (1972). · doi:10.1090/S0002-9939-1972-0295126-2
[122] B. Fuglede, ?A commutativity theorem for normal operators,? Proc. Amer. Mali. Soc.,36, 35?40 (1950). · Zbl 0035.35804 · doi:10.1073/pnas.36.1.35
[123] B. Fuglede and R. Kadison, ?Determinant theory in finite factors,? Ann. Math.55, No. 3, 520?530 (1952). · Zbl 0046.33604 · doi:10.2307/1969645
[124] F. Gilfeather, ?On the Suzuki structure theory fornonself-adjoint operators on Hilbert space,? Acta Sci. Math.,32, Nos. 3?4, 239?250 (1971). · Zbl 0245.47019
[125] J. Glimm, ?A Stone-Weierstrass theorem for C*-algebras,? Ann. Math.,72, No. 2, 216?244 (1960). · Zbl 0097.10705 · doi:10.2307/1970133
[126] R. Goodman, ?Invariant subspaces for normal operators,? J. Math. Mech.,15, No. 1, 123?128 (1966). · Zbl 0132.35801
[127] P. R. Halmos, ?Invariant subspaces for polynomially compact operators,? Pacif. J. Math.,16, No. 3, 433?437 (1966). · Zbl 0141.12904 · doi:10.2140/pjm.1966.16.433
[128] P. R. Halmos, ?Quasitriangular operators,? Acta Sci. Math.,29, Nos. 3?4, 283?294 (1968).
[129] P. R. Halmos, ?Invariant subspaces. Abstract spaces and approximation,? Proc. M. R. I. Oberwolfach, Birkhäuser, Basel (1968), pp. 26?30.
[130] P. R. Halmos, ?Capacity in Banach algebras,? Indiana Univ. Math. J.,20, No. 9, 855?863 (1971). · Zbl 0196.14803 · doi:10.1512/iumj.1971.20.20067
[131] K. J. Harrison, ?Transitive atomic lattices of subspaces,? Indiana Univ. Math. J.,21, No. 7, 621?642 (1972). · Zbl 0255.47006 · doi:10.1512/iumj.1972.21.21049
[132] K. J. Harrison, H. Radjavi, and P. Rosenthal, ?A transitive medial subspace lattice,? Proc. Amer. Math. Soc.,28, No. 1, 119?121 (1971). · Zbl 0211.44402 · doi:10.1090/S0002-9939-1971-0283609-X
[133] H. Helson and D. Lowdenslager, ?Prediction theory and Fourier series in several variables,? Acta Math.,99, Nos. 3?4, 165?202 (1958). · Zbl 0082.28201 · doi:10.1007/BF02392425
[134] D. A. Herrero, ?A pathological lattice of invariant subspaces,? J. Funct. Anal.,11, No. 2, 131?137 (1972). · Zbl 0255.47007 · doi:10.1016/0022-1236(72)90083-3
[135] D. A. Herrero, ?Operator algebras of finite strict multiplicity,? Indiana Univ. Math. J.,22, No. 1, 13?24 (1972). · doi:10.1512/iumj.1973.22.22003
[136] D. A. Herrero, ?Algebras de operadores transitivas que contienen una subalgebra de multiplicidad estricta finita,? Rev. Union Mat. Argent.,26, No. 2, 77?84 (1972).
[137] D. A. Herrero and N. Salinas, ?Analytically-invariant and bi-invariant subspaces,? Trans. Amer. Math. Soc.,173, Nov., 117?136 (1972). · Zbl 0253.46126 · doi:10.1090/S0002-9947-1972-0312294-9
[138] R. A. Hirshfeld, ?On polynomials in several Hilbert space operators,? Math. Z.,127, No. 3, 224?234 (1972). · Zbl 0256.47004 · doi:10.1007/BF01114926
[139] J. A. R. Holbrook, ?Spectral dilations and polynomially bounded operators,? Indiana Univ. Math. J.,20, No. 11, 1027?1034 (1971). · Zbl 0219.47006 · doi:10.1512/iumj.1971.20.20098
[140] T. B. Hoover, ?Hyperinvariant subspaces for n-normal operators,? Acta Sci. Math.,32, Nos. 1?2, 109?119 (1971). · Zbl 0228.47026
[141] T. B. Hoover, ?Operator algebras with complemented invariant subspace lattices,? Indiana Univ. Math. J.,22, No. 11, 1029?1035 (1973). · Zbl 0259.46054 · doi:10.1512/iumj.1973.22.22086
[142] T. B. Hoover, ?Operator algebras with reducing invariant subspaces,? Pacif. J. Math.,44, No. 1, 173?179 (1973). · Zbl 0259.46052 · doi:10.2140/pjm.1973.44.173
[143] A. Hopenwasser, ?Isometries on irreducible triangular operator algebras,? Math. Scand.,30, No. 1, 136?140 (1972). · Zbl 0239.46073 · doi:10.7146/math.scand.a-11069
[144] A. Hopenwasser, ?Completely isometric maps and triangular operator algebras,? Proc. London Math. Soc.,25, No. 1, 96?114 (1972). · Zbl 0235.46097 · doi:10.1112/plms/s3-25.1.96
[145] T. Itô, ?On the commutative family of subnormal operators,? J. Fac. Sci. Hokkaido Univ., Ser. 1,14, 1?15 (1958). · Zbl 0089.32302
[146] B. E. Johnson and A. L. Shields, ?Hyperinvariant subspaces for operators on the space of complex sequences,? Mich. Math. J.,19, No. 2, 189?191 (1972). · Zbl 0222.47001 · doi:10.1307/mmj/1029000853
[147] R. E. Johnson, ?Distinguished rings of linear transformations,? Trans. Amer. Math. Soc.,111, 400?412 (1964). · doi:10.1090/S0002-9947-1964-0161884-0
[148] R. V. Kadison and J. M. Singer, ?Triangular operator algebras,? Amer. J. Math.,82, No. 2, 227?259 (1960). · Zbl 0096.31703 · doi:10.2307/2372733
[149] G. Kalisch, ?On similarity, reducing manifolds, and unitary equivalence of certain Volterra operators,? Ann. Math.,66, No. 3, 481?494 (1957). · Zbl 0078.09602 · doi:10.2307/1969905
[150] N. Kamei, ?Simply invariant subspace theorem for antisymmetric subdiagonal algebras,? Tôhoku Math. J.,21, No. 3, 467?473 (1969). · Zbl 0192.48201 · doi:10.2748/tmj/1178242957
[151] K.-M. Körber, ?Die invarianten Teilräume der stetigen Endomorphismen von ?,? Math. Ann.,182, No. 2, 95?103 (1969). · Zbl 0181.14002 · doi:10.1007/BF01376216
[152] A. Lambert, ?Strictly cyclic weighted shifts,? Proc. Amer. Math. Soc.,29, No. 2, 331?336 (1972). · Zbl 0214.14201 · doi:10.1090/S0002-9939-1971-0275213-4
[153] A. Lambert, ?Strictly cyclic operator algebras,? Pacif. J. Math.,39, No. 3, 717?726 (1971). · Zbl 0213.40701 · doi:10.2140/pjm.1971.39.717
[154] A. Lambert, ?Spectral properties of strictly cyclic operator algebras,? Indiana Univ. Math. J.,22, No. 10, 959?963 (1973). · Zbl 0281.46057 · doi:10.1512/iumj.1973.22.22080
[155] A. Lambert, ?The algebra generated by an invertibly weighted shift,? J. London Math. Soc.,5, No. 4, 741?747 (1972). · Zbl 0244.46079 · doi:10.1112/jlms/s2-5.4.741
[156] E. C. Lance, ?Some properties of nest algebras,? Proc. London Math. Soc.,19, No. 1, 45?68 (1969). · Zbl 0169.17502 · doi:10.1112/plms/s3-19.1.45
[157] P. D. Lax, ?Translation invariant subspaces,? Acta Math.,101, Nos. 3?4, 163?178 (1959). · Zbl 0085.09102 · doi:10.1007/BF02559553
[158] A. Lebow, ?On von Neumann’s theory of spectral sets,? J. Math. Anal. and Appl.,7, No. 1, 64?90 (1963). · Zbl 0145.39301 · doi:10.1016/0022-247X(63)90078-7
[159] R. Leggett, ?On the invariant subspace structure of compact dissipative operators,? Indiana Univ. Math. J.,22, No. 10, 919?928 (1973). · Zbl 0258.47007 · doi:10.1512/iumj.1973.22.22076
[160] G. Lumer, ?States, quotient algebras and invariant subspaces,? C. R. Acad. Sci.,274, No. 17, A1308-A1311 (1972). · Zbl 0231.46087
[161] G. Lumer and M. Rosenblum, ?Linear operator equations,? Proc. Amer. Math. Soc.,10, No. 1, 32?41 (1959). · Zbl 0133.07903 · doi:10.1090/S0002-9939-1959-0104167-0
[162] M. A. Naimark, ?On commuting unitary operators in spaces with indefinite metric,? Acta Sci. Math.,24, Nos. 3?4, 177?189 (1963). · Zbl 0115.33301
[163] M. A. Naimark, ?Kommutative symmetrische Operatorenalgebren in Pontrjyaginschen Raumen IIk,? Math. Ann.,162, No. 1, 147?171 (1965). · Zbl 0137.10303 · doi:10.1007/BF01361941
[164] J. von Neumann, ?On rings of operators, III,? Ann. Math.,41, 94?161 (1940). · Zbl 0023.13303 · doi:10.2307/1968823
[165] J. von Neumann, ?Eine Spectralthoerie für allgemeine Operatoren eines unitären Raumes,? Math. Nach.,4, 258?281 (1951). · Zbl 0042.12301
[166] E. A. Nordgren, ?Invariant subspaces of a direct sum of weighted shifts,? Pacif. J. Math.,27, No. 3, 587?598 (1968). · Zbl 0172.16804 · doi:10.2140/pjm.1968.27.587
[167] E. A. Nordgren, ?Transitive algebras,? Indiana Univ. Math. J.,20, No. 10, 925?927 (1971). · Zbl 0215.20602 · doi:10.1512/iumj.1971.20.20081
[168] E. A. Nordgren, ?Transitive operator algebras,? J. Math. Anal. Appl.,32, No. 3, 639?643 (1970). · Zbl 0206.43203 · doi:10.1016/0022-247X(70)90287-8
[169] E. A. Nordgren, H. Radjavi, and P. Rosenthal, ?On density of transitive algebras,? Acta. Sci. Math.,3, Nos. 3?4 (1969). · Zbl 0184.15905
[170] E. A. Nordgren and P. Rosenthal, ?Algebras containing unilateral shifts or finite-rank operators,? Duke Math. J.,40, No. 2, 419?424 (1973). · Zbl 0273.46055 · doi:10.1215/S0012-7094-73-04034-9
[171] S. Parrot, ?Unitary dilations for commuting contractions,? Pacif. J. Math.,34, No. 2, 481?490 (1970). · Zbl 0202.41802 · doi:10.2140/pjm.1970.34.481
[172] C. Pearcy, ?On certain von Neumann algebras which are generated by partial isometries,? Proc. Amer. Soc.,15, No. 3, 393?395 (1964). · Zbl 0135.16803 · doi:10.1090/S0002-9939-1964-0161172-8
[173] C. Pearcy and N. Salinas, ?An invariant-subspace theorem,? Mich. Math. J.,20, No. 1, 23?31 (1973). · Zbl 0258.47006
[174] F. M. Pollack, ?Properties of the matrix range of an operator,? Indiana Univ. Math. J.,22, No. 5, 419?427 (1972). · doi:10.1512/iumj.1973.22.22037
[175] H. Radjavi and P. Rosenthal, ?Invariant subspaces and weakly closed algebras,? Bull. Amer. Math. Soc.,74, No. 5, 1013?1014 (1968). · Zbl 0167.43302 · doi:10.1090/S0002-9904-1968-12118-4
[176] H. Radjavi and P. Rosenthal, ?On invariant subspaces and reflexive algebras,? Amer. J. Math.,51, No. 1, 683?692 (1969). · Zbl 0187.06201 · doi:10.2307/2373347
[177] H. Radjavi and P. Rosenthal, ?On reflexive algebras of operators,? Indiana Univ. Math. J.,20, No. 10, 935?937 (1971). · Zbl 0215.20603 · doi:10.1512/iumj.1971.20.20083
[178] H. Radjavi and P. Rosenthal, ?A sufficient condition that an operator algebra be self-adjoint,? Can. J. Math.,23, No. 4, 588?597 (1971). · Zbl 0218.46063 · doi:10.4153/CJM-1971-066-7
[179] H. Radjavi and P. Rosenthal, ?Hyperinvariant subspaces for spectral and n-normal operators,? Acta Sci. Math.,32, Nos. 1?2, 121?126 (1971). · Zbl 0229.47004
[180] C. E. Rickart, ?The uniqueness of norm problem in Banach algebras,? Ann. Math.,51, 615?628 (1950). · Zbl 0037.20003 · doi:10.2307/1969371
[181] J. R. Ringrose, ?On some algebras of operators,? Proc. London Math. Soc.,15, No. 3, 61?83 (1965). · Zbl 0135.16804 · doi:10.1112/plms/s3-15.1.61
[182] J. R. Ringrose, ?Algebraic isomorphisms between ordered bases,? Amer. J. Math.,83, No. 3, 463?478 (1961). · Zbl 0100.11602 · doi:10.2307/2372889
[183] J. R. Ringrose, ?On some algebras of operators, II,? Proc. London Math. Soc.,16, No. 3, 385?402 (1966). · Zbl 0156.14301 · doi:10.1112/plms/s3-16.1.385
[184] P. Rosenthal, ?A note on unicellular operators,? Proc. Amer. Math. Soc.,19, No. 2, 505?506 (1968). · Zbl 0161.34503
[185] P. Rosenthal, ?Completely reducible operators,? Proc. Amer. Math. Soc.,19, No. 4, 826?830 (1968). · Zbl 0164.16501 · doi:10.1090/S0002-9939-1968-0231234-9
[186] P. Rosenthal, ?Examples of invariant subspace lattices,? Duke Math. J.,37, No. 1, 103?112 (1970). · Zbl 0198.45601 · doi:10.1215/S0012-7094-70-03715-4
[187] P. Rosenthal, ?Remarks on invariant subspace lattices,? Can. Math. Bull.,12, No. 5, 639?643 (1969). · Zbl 0186.45205 · doi:10.4153/CMB-1969-082-1
[188] P. Rosenthal, ?Weakly closed maximal triangular algebras are hyperreducible,? Proc. Amer. Math. Soc.,24, No. 1, 220 (1970). · Zbl 0187.06202
[189] T. Saitô, ?Some remarks to Andô’s theorem,? Tôhoku Math. J.,18, No. 4, 404?409 (1966). · Zbl 0145.39101 · doi:10.2748/tmj/1178243382
[190] D. E. Sarason, ?A remark on the Volterra operators,? J. Math. Anal. Appl.,12, No. 2, 244?246 (1965). · Zbl 0138.38801 · doi:10.1016/0022-247X(65)90035-1
[191] D. E. Sarason, ?Invariant subspaces and unstarred operator algebras,? Pacif. J. Math.,17, No. 3, 511?517 (1966). · Zbl 0171.33703 · doi:10.2140/pjm.1966.17.511
[192] D. E. Sarason, ?Weak-star density of polynomials,? J. Reine Angew. Math.,252, 1?15 (1972). · Zbl 0242.46023
[193] H. Schaefer, ?Eine Bemerkung zur Existenz invaruanter Tailräume linearer Abbildungen,? Math. Z.,82, No. 1, 90 (1963). · Zbl 0123.31301 · doi:10.1007/BF01112826
[194] M. Schreiber, ?A functional calculus for general operators in Hilbert space,? Trans. Amer. Math. Soc.,87, No. 1, 108?118 (1958). · doi:10.1090/S0002-9947-1958-0099601-2
[195] J. T. Schwartz, ?On spectral operators in Hilbert space with compact imaginary part,? Commun. Pure Appl. Math.,15, No. 1, 95?97 (1962). · Zbl 0105.31201 · doi:10.1002/cpa.3160150108
[196] J. T. Schwartz, ?Subdiagonalization of operators in Hilbert space with compact imaginary part,? Commun. Pure Appl. Math.,15, No. 2, 159?172 (1962). · Zbl 0111.11303 · doi:10.1002/cpa.3160150205
[197] J. T. Scroggs, ?Invariant subspaces of a normal operator,? Duke Math. J.,26, No. 1, 85?112 (1959). · Zbl 0084.11001 · doi:10.1215/S0012-7094-59-02609-2
[198] I. Segal, ?A noncommutative extension of abstract integration,? Ann. Math.,57, No. 3, 401?457 (1953). · Zbl 0051.34201 · doi:10.2307/1969729
[199] A. L. Shields, ?A note on invariant subspaces,? Mich. Math. J.,17, No. 3, 231?233 (1970). · Zbl 0187.37806 · doi:10.1307/mmj/1029000470
[200] T. Srinivasan and J. Wang, ?Weak* Dirichlet algebras,? Symposium on Function Algebras, Scott-Foresman (1966). · Zbl 0191.13603
[201] W. Stinespring, ?Positive functions on C*-algebras,? Proc. Amer. Math. Soc.,6, No. 2, 211?216 (1955). · Zbl 0064.36703
[202] N. Suzuki, ?Algebraic aspects of non-self-adjoint operators,? Proc. Japan. Acad.,41, No. 8, 706?710 (1965). · Zbl 0144.17503 · doi:10.3792/pja/1195522300
[203] N. Suzuki, ?The algebraic structure of non-self-adjoint operators,? Acta Sci. Math.,27, Nos. 3?4, 173?184 (1966). · doi:10.1016/S0076-5392(09)60416-1
[204] N. Suzuki, ?The structure of spectral operators with completely continuous imaginary part,? Proc. Amer. Math. Soc.,22, No. 1, 82?84 (1969). · Zbl 0176.11203 · doi:10.1090/S0002-9939-1969-0247517-3
[205] N. Suzuki, ?Reduction theory of operators on Hilbert space. The invariant subspace problem,? Indiana Univ. Math. J.,20, No. 10, 953?958 (1971). · Zbl 0226.47004 · doi:10.1512/iumj.1971.20.20089
[206] B. Sz.-Nagy, ?On uniformly bounded linear operators in Hilbert space,? Acta Sci. Math.,11, 152?157 (1947). · Zbl 0029.30501
[207] B. Sz.-Nagy ?Contractions of Hilbert space,? Acta Sci. Math.,15, No. 1, 87?92 (1953).
[208] B. Sz.-Nagy, ?Transformations of Hilbert space and positive-type functions on a group,? Acta Sci. Math.,15, No. 2, 104?114 (1954).
[209] B. Sz.-Nagy and C. Foias, ?Quasi-similarity between operators and invariant subspaces,? C. R. Acad. Sci.,261, No. 20, 3938?3940 (1965).
[210] B. Sz.-Nagy and C. Foias, ?Contractions of Hilbert space. III,? Acta Sci. Math.,19, Nos. 1?2, 26?46 (1958).
[211] B. Sz.-Nagy and C. Foias, ?Contractions of Hilbert space. IV,? Acta Sci. Math.,21, Nos. 3?4, 251?259 (1960).
[212] B. Sz.-Nagy and C. Foias, ?Contractions of Hilbert space. VI. Functional calculus,? Acta Sci. Math.,23, Nos. 1?2, 130?167 (1962).
[213] B. Sz.-Nagy and C. Foias, ?Contractions of Hilbert space. VII. Canonical triangulation. Minimal functions,? Acta Sci. Math.,25, Nos. 1?2, 12?37 (1964).
[214] B. Sz.-Nagy and C. Foias, ?Contractions of Hilbert Space, VIII. Characteristic functions. Functional models,? Acta Sci. Math.,25, Nos. 1?2, 38?72 (1964).
[215] B. Sz.-Nagy and C. Foias, ?Operators without multiplicity,? Acta. Sci. Math.,30, Nos. 1?2, 1?18 (1969).
[216] B. Sz.-Nagy and C. Foias, ?Jordan model for a class of operators in Hilbert space,? Acta Sci. Math.,31, Nos. 1?2, 91?115 (1970).
[217] B. Sz.-Nagy and C. Foias, ?Cyclic and quasi-affine vectors,? Stud. Math.,31, No. 1, 35?42 (1968).
[218] D. K. Taylor, ?Interpolation in algebras of operator fields,? J. Funct. Anal.,10, No. 2, 159?190 (1972). · Zbl 0245.46083 · doi:10.1016/0022-1236(72)90047-X
[219] Jun Tomiyama, ?On some types of maximal Abelian subalgebras,? J. Funct. Anal.,10, No. 4, 373?386 (1972). · Zbl 0244.46076 · doi:10.1016/0022-1236(72)90035-3
[220] J. Wermer, ?On invariant subspaces of normal operators,? Proc. Amer. Math. Soc.,2, 270?277 (1952). · Zbl 0046.33704 · doi:10.1090/S0002-9939-1952-0048700-X
[221] N. Wiener, ?On the factorization of matrices,? Comment. Math. Helv.,29, No. 2, 97?111 (1955). · Zbl 0064.06301 · doi:10.1007/BF02564273
[222] B. Yood, ?Additive groups and linear manifolds of transformations between Banach spaces,? Amer. J. Math.,71, 663?677 (1949). · Zbl 0034.06303 · doi:10.2307/2372357
[223] Takashi Yoshino, ?Subnormal operator with a cyclic vector,? Tôhoku Math. J.,21, No. 1, 47?55 (1969). · Zbl 0192.47801 · doi:10.2748/tmj/1178243033
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.