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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0773052-3
PII: S 0002-9947(1985)0773052-3
Article copyright: © Copyright 1985 American Mathematical Society