A reflexivity theorem for weakly closed subspaces of operators

Author:
Hari Bercovici

Journal:
Trans. Amer. Math. Soc. **288** (1985), 139-146

MSC:
Primary 47D15; Secondary 47A15

DOI:
https://doi.org/10.1090/S0002-9947-1985-0773052-3

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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Greg Robel,*On the structure of (BCP)-operators and related algebras. II*, J. Operator Theory**12**(1984), no. 2, 235–245. MR**757433**

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0773052-3

Article copyright:
© Copyright 1985
American Mathematical Society