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 and are reflexive proper linear subspaces of operators acting on a separable Hilbert space, then the hyperreflexivity constant of is at least as great as the product of the constants of and .

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Additional Information

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