Hyperreflexivity and a dual product construction

Larson, David R.

doi:10.1090/S0002-9947-1986-0819936-X

Hyperreflexivity and a dual product construction
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by David R. Larson PDF

Trans. Amer. Math. Soc. 294 (1986), 79-88 Request permission

Abstract:

We show that an example of a nonhyperreflexive CSL algebra recently constructed by Davidson and Power is a special case of a general and natural reflexive subspace construction. Completely different techniques of proof are needed because of absence of symmetry. It is proven that if $\mathcal {S}$ and $\mathcal {I}$ are reflexive proper linear subspaces of operators acting on a separable Hilbert space, then the hyperreflexivity constant of ${({\mathcal {S}_ \bot } \otimes {\mathcal {I}_ \bot })^ \bot }$ is at least as great as the product of the constants of $\mathcal {S}$ and $\mathcal {I}$.

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