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Book Review
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Book Information
Author(s):
Bernard Beauzamy
Title:
Introduction to operator theory and invariant subspaces
Additional book information:
North-Holland, Amsterdam, New York, Oxford, Tokyo, 1988, xiv + 358 pp., $84.25. ISBN 0-444-7052-X
References:
- 1.
- C. Apostol, Ultraweakly closed operator algebras, J. Operator Theory 2 (1979), 49-61. MR 553863
- 2.
- C. Apostol, C. Foiaş, and D. Voiculescu, Some results on nonquasitriangular operators. IV, Rev. Roumaine Math. Pures Appl. 43 (1973), 487-514.
- 3.
- N. Aronszajn and K. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. (2) 60 (1954), 345-350. MR 65807
- 4.
- W. Arveson, Ten lectures on operator algebras, CBMS Regional Conf. Ser. in Math., no. 55, Amer. Math. Soc., Providence, R. I., 1984. MR 762819
- 5.
- B. Beauzamy, Sous-espaces invariants de type fonctionnel dans les espaces de Banach, Acta Math. 144 (1981), 27-64. MR 571478
- 6.
- B. Beauzamy, Un opérateur sans sous-espace invariant nontrivial: simplification de l'exemple de P. Enflo, Integral Equations Operator Theory 8 (1985), 314-384. MR 792905
- 7.
- S. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), 310-333. MR 511974
- 8.
- S. Brown, B. Chevreau, and C. Pearcy, Contractions with rich spectrum have invariant subspaces, J. Operator Theory 1 (1979), 123-136. MR 526294
- 9.
- S. Brown, B. Chevreau, and C. Pearcy, On the structure of contraction operators. II, J. Funct. Anal. 76 (1988), 30-55. MR 923043
- 10.
- R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972. MR 361893
- 11.
- N. Dunford and J. T. Schwartz, Linear operators, Part II: Spectral theory, Interscience, New York, 1963. MR 188745
- 12.
- P. Enflo, On the invariant subspace problem in Banach spaces, Acta Math. 158 (1987), 213-313. MR 892591
- 13.
- I. C. Gohberg and M. G. Krein, The theory of Volterra operators in Hilbert space, "Nauka", Moscow, 1967. (Russian) MR 218923
- 14.
- P. R. Halmos, Quasitriangular operators, Acta Sci. Math. (Szeged) 29 (1968), 283-293. MR 234310
- 15.
- P. R. Halmos, A Hilbert space problem book, Second ed., Springer-Verlag, New York, 1982. MR 675952
- 16.
- C. Read, A solution to the invariant subspace problem, Bull. London Math. Soc. 16(1984), 337-401. MR 749447
Additional Information:
Reviewer(s):
Hari
Bercovici
Review Information:
Journal:
Bull. Amer. Math. Soc.
22
(1990),
148-152.
DOI:
10.1090/S0273-0979-1990-15867-7
PII:
S 0273-0979(1990)15867-7
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