Bulletin of the American Mathematical Society

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Book Information:

Author: 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.

Constantin Apostol, Ultraweakly closed operator algebras, J. Operator Theory 2 (1979), no. 1, 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.

N. Aronszajn and K. T. Smith, Invariant subspaces of completely continuous operators, Ann. of Math. (2) 60 (1954), 345–350. MR 65807, DOI 10.2307/1969637

William Arveson, Ten lectures on operator algebras, CBMS Regional Conference Series in Mathematics, vol. 55, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1984. MR 762819, DOI 10.1090/cbms/055

B. Beauzamy, Sous-espaces invariants de type fonctionnel dans les espaces de Banach, Séminaire d’Analyse Fonctionnelle (1978–1979), École Polytech., Palaiseau, 1979, pp. Exp. No. 27, 25 (French). MR 557379

B. Beauzamy, Un opérateur sans sous-espace invariant: simplification de l’exemple de P. Enflo, Integral Equations Operator Theory 8 (1985), no. 3, 314–384 (French). MR 792905, DOI 10.1007/BF01202903

Scott W. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), no. 3, 310–333. MR 511974, DOI 10.1007/BF01682842

S. Brown, B. Chevreau, and C. Pearcy, Contractions with rich spectrum have invariant subspaces, J. Operator Theory 1 (1979), no. 1, 123–136. MR 526294

Bernard Chevreau and Carl Pearcy, On the structure of contraction operators. I, J. Funct. Anal. 76 (1988), no. 1, 1–29. MR 923042, DOI 10.1016/0022-1236(88)90046-8

Ronald G. Douglas, Banach algebra techniques in operator theory, Pure and Applied Mathematics, Vol. 49, Academic Press, New York-London, 1972. MR 0361893

Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745

Per Enflo, On the invariant subspace problem for Banach spaces, Acta Math. 158 (1987), no. 3-4, 213–313. MR 892591, DOI 10.1007/BF02392260

I. C. Gohberg and M. G. Kreĭn, Teoriya vol′terrovykh operatorov v gil′bertovom prostranstve i ee prilozheniya, Izdat. “Nauka”, Moscow, 1967 (Russian). MR 0218923

P. R. Halmos, Quasitriangular operators, Acta Sci. Math. (Szeged) 29 (1968), 283–293. MR 234310

Paul Richard Halmos, A Hilbert space problem book, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 17, Springer-Verlag, New York-Berlin, 1982. MR 675952

C. J. Read, A solution to the invariant subspace problem, Bull. London Math. Soc. 16 (1984), no. 4, 337–401. MR 749447, DOI 10.1112/blms/16.4.337

1.

C. Apostol, Ultraweakly closed operator algebras, J. Operator Theory 2 (1979), 49-61. MR 0553863

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