A reflexivity theorem for weakly closed subspaces of operators

Bercovici, Hari

doi:10.1090/S0002-9947-1985-0773052-3

A reflexivity theorem for weakly closed subspaces of operators
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Trans. Amer. Math. Soc. 288 (1985), 139-146 Request permission

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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