×

zbMATH — the first resource for mathematics

A survey of the theory of spectral operators. (English) Zbl 0088.32102

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] William G. Bade, Unbounded spectral operators, Pacific J. Math. 4 (1954), 373 – 392. · Zbl 0056.34801
[2] William G. Bade, Weak and strong limits of spectral operators, Pacific J. Math. 4 (1954), 393 – 413. · Zbl 0056.34802
[3] William G. Bade, On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345 – 360. · Zbl 0066.36202
[4] William G. Bade, A multiplicity theory for Boolean algebras of projections in Banach spaces, Trans. Amer. Math. Soc. 92 (1959), 508 – 530. · Zbl 0086.31501
[5] George D. Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Trans. Amer. Math. Soc. 9 (1908), no. 4, 373 – 395. · JFM 39.0386.02
[6] Jean Dieudonné, Sur la théorie spectrale, J. Math. Pures Appl. (9) 35 (1956), 175 – 187 (French). · Zbl 0071.33202
[7] Nelson Dunford, Spectral theory, Bull. Amer. Math. Soc. 49 (1943), 637 – 651. · Zbl 0063.01184
[8] Nelson Dunford, Spectral theory. I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185 – 217. · Zbl 0063.01185
[9] Nelson Dunford, Spectral theory in abstract spaces and Banach algebras, Proceedings of the Symposium on Spectral Theory and Differential Problems, Oklahoma Agricultural and Mechanical College, Stillwater, Okla., 1951, pp. 1 – 65.
[10] Nelson Dunford, Spectral theory, Proceedings of the Symposium on Spectral Theory and Differential Problems, Oklahoma Agricultural and Mechanical College, Stillwater, Okla., 1951, pp. 203 – 208.
[11] Nelson Dunford, The reduction problem in spectral theory, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R. I., 1952, pp. 115 – 122.
[12] Nelson Dunford, Spectral theory. II. Resolutions of the identity, Pacific J. Math. 2 (1952), 559 – 614. · Zbl 0047.35903
[13] Nelson Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321 – 354. · Zbl 0056.34601
[14] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402
[15] Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Spectral theory. Selfadjoint operators in Hilbert space; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1963 original; A Wiley-Interscience Publication. Nelson Dunford and Jacob T. Schwartz, Linear operators. Part III, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Spectral operators; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1971 original; A Wiley-Interscience Publication.
[16] S. R. Foguel, Sums and products of commuting spectral operators, Ark. Mat. 3 (1958), 449 – 461. · Zbl 0081.12301
[17] S. R. Foguel, The relations between a spectral operator and its scalar part, Pacific J. Math. 8 (1958), 51 – 65. · Zbl 0080.32802
[18] S. R. Foguel, Normal operators of finite multiplicity, Comm. Pure Appl. Math. 11 (1958), 297 – 313. · Zbl 0084.33901
[19] S. R. Foguel, A perturbation theorem for scalar operators, Comm. Pure Appl. Math. 11 (1958), 293 – 295. · Zbl 0084.33801
[20] Ivar Fredholm, Sur une classe d’équations fonctionnelles, Acta Math. 27 (1903), no. 1, 365 – 390 (French). · JFM 34.0422.02
[21] K. O. Friedrichs, On the perturbation of continuous spectra, Communications on Appl. Math. 1 (1948), 361 – 406. · Zbl 0031.31204
[22] T. H. Hildebrandt, Über vollstetige lineare Transformationen, Acta Math. 51 (1928), no. 1, 311 – 318 (German). · JFM 54.0427.03
[23] Shizuo Kakutani, An example concerning uniform boundedness of spectral measures, Pacific J. Math. 4 (1954), 363 – 372. · Zbl 0056.34702
[24] Henry P. Kramer, Perturbation of differential operators, Pacific J. Math. 7 (1957), 1405 – 1435. · Zbl 0079.13602
[25] E. R. Lorch, Bicontinuous linear transformations in certain vector spaces, Bull. Amer. Math. Soc. 45 (1939), 564 – 569. · Zbl 0022.05302
[26] G. W. Mackey, Commutative Banach algebras, Mimeographed lecture notes, Harvard University, 1952.
[27] Jürgen Moser, Störungstheorie des kontinuierlichen Spektrums für gewöhnliche Differentialgleichungen zweiter Ordnung, Math. Ann. 125 (1953), 366 – 393 (German). · Zbl 0050.31304
[28] M. A. Naĭmark, Investigation of the spectrum and expansion in eigenfunctions of singular nonselfadjoint differential operators of the second order, Uspehi Matem. Nauk (N.S.) 8 (1953), no. 4(56), 174 – 175 (Russian).
[29] M. A. Naĭmark, On expansion in characteristic functions of non-self-adjoint singular differential operators of the second order, Doklady Akad. Nauk SSSR (N.S.) 89 (1953), 213 – 216 (Russian).
[30] M. A. Naĭmark, Investigation of the spectrum and the expansion in eigenfunctions of a nonselfadjoint operator of the second order on a semi-axis, Trudy Moskov. Mat. Obšč. 3 (1954), 181 – 270 (Russian).
[31] B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277 – 304. · Zbl 0019.41603
[32] Friedrich Riesz, Über lineare Funktionalgleichungen, Acta Math. 41 (1916), no. 1, 71 – 98 (German). · JFM 46.0635.01
[33] J. Schauder, Über lineare, vollstetige Funktional-operationen, Studia Math. vol. 2 (1930) pp. 183-196. · JFM 56.0354.01
[34] J. Schwartz, Perturbations of spectral operators, and applications. I. Bounded perturbations, Pacific J. Math. 4 (1954), 415 – 458. · Zbl 0056.34901
[35] J. Schwartz, Two perturbation formulae, Comm. Pure Appl. Math. 8 (1955), 371 – 376. · Zbl 0065.10501
[36] D. R. Smart, Eigenfunction expansions in \?^{\?} and \?, Illinois J. Math. 3 (1959), 82 – 97. · Zbl 0084.33802
[37] John Wermer, Commuting spectral measures on Hilbert space, Pacific J. Math. 4 (1954), 355 – 361. · Zbl 0056.34701
[38] John Wermer, On restrictions of operators, Proc. Amer. Math. Soc. 4 (1953), 860 – 865. · Zbl 0052.12106
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.