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
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 , 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 , and applies even to linear spaces of operators. Our result contains the reflexivity theorems of [3,2 and 9] as particular cases.
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 [1]
 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).
 [2]
 H. Bercovici, B. Chevreau, C. Foias and C. Pearcy, Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II, Math. Z. 187 (1984), 97103. MR 753424 (85k:47090)
 [3]
 H. Bercovici, C. Foias, J. Langsam and C. Pearcy, operators are reflexive, Michigan Math. J. 29 (1982), 371379. MR 674290 (84a:47007)
 [4]
 H. Bercovici, C. Foias and C. Pearcy, Factoring traceclass operatorvalued functions with applications to the class , J. Operator Theory (to appear). MR 808297 (87a:47014)
 [5]
 , Dilation theory and systems of simultaneous equations in the predual of an operator algebra. I, Michigan Math. J. 30 (1983), 335354. MR 725785 (85k:47089)
 [6]
 A. Brown and C. Pearcy, Introduction to operator theory. I. Elements of functional analysis, Springer, New York, 1977. MR 0511596 (58:23463)
 [7]
 D. W. Hadwin and E. A. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982), 323. MR 650190 (83f:47033)
 [8]
 A. I. Loginov and V. S. Sulman, Hereditary and intermediate reflexivity of algebras, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 12601273. (Russian) MR 0405124 (53:8919)
 [9]
 G. Robel, On the structure of operators and related algebras. I, J. Operator Theory 12 (1984), 2345. MR 757111 (86f:47011a)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198507730523
PII:
S 00029947(1985)07730523
Article copyright:
© Copyright 1985
American Mathematical Society
