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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Hyperreflexivity and a dual product construction


Author: David R. Larson
Journal: Trans. Amer. Math. Soc. 294 (1986), 79-88
MSC: Primary 47D25; Secondary 46L99, 47A15, 47D35
DOI: https://doi.org/10.1090/S0002-9947-1986-0819936-X
MathSciNet review: 819936
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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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DOI: https://doi.org/10.1090/S0002-9947-1986-0819936-X
Keywords: Reflexive operator algebra, hyperreflexive, tensor product, dual product, distance constant, preannihilator
Article copyright: © Copyright 1986 American Mathematical Society