A reflexivity theorem for weakly closed subspaces of operators
Author:
Hari Bercovici
Journal:
Trans. Amer. Math. Soc. 288 (1985), 139146
MSC:
Primary 47D15; Secondary 47A15
DOI:
https://doi.org/10.1090/S00029947198507730523
MathSciNet review:
773052
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Abstract: It was proved in [4] that the ultraweakly closed algebras generated by certain contractions on Hilbert space have a remarkable property. This property, in conjunction with the fact that these algebras are isomorphic to ${H^\infty }$, was used in [3] to show that such ultraweakly closed algebras are reflexive. In the present paper we prove an analogous result that does not require isomorphism with ${H^\infty }$, and applies even to linear spaces of operators. Our result contains the reflexivity theorems of [3,2 and 9] as particular cases.

C. Apostol, H. Bercovoci, C. Foias and C. Pearcy, Invariant subspaces, dilation theory, and the structure of the predual of a dual operator algebra. I, J. Functional Anal. (to appear).
 Hari Bercovici, Bernard Chevreau, Ciprian Foias, and Carl Pearcy, Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II, Math. Z. 187 (1984), no. 1, 97–103. MR 753424, DOI https://doi.org/10.1007/BF01163170
 H. Bercovici, C. Foiaş, J. Langsam, and C. Pearcy, (BCP)operators are reflexive, Michigan Math. J. 29 (1982), no. 3, 371–379. MR 674290
 H. Bercovici, C. Foias, and C. Pearcy, Factoring traceclass operatorvalued functions with applications to the class ${\scr A}_{\aleph _0}$, J. Operator Theory 14 (1985), no. 2, 351–389. MR 808297
 H. Bercovici, C. Foias, and C. Pearcy, Dilation theory and systems of simultaneous equations in the predual of an operator algebra. I, Michigan Math. J. 30 (1983), no. 3, 335–354. MR 725785, DOI https://doi.org/10.1307/mmj/1029002909
 Arlen Brown and Carl Pearcy, Introduction to operator theory. I, SpringerVerlag, New YorkHeidelberg, 1977. Elements of functional analysis; Graduate Texts in Mathematics, No. 55. MR 0511596
 D. W. Hadwin and E. A. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), no. 1, 3–23. MR 650190
 A. N. Loginov and V. S. Šul′man, Hereditary and intermediate reflexivity of $W^ *$algebras, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 6, 1260–1273, 1437 (Russian). MR 0405124
 Greg Robel, On the structure of (BCP)operators and related algebras. I, J. Operator Theory 12 (1984), no. 1, 23–45. MR 757111
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© Copyright 1985
American Mathematical Society