Hyperreflexivity and a dual product construction

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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 S \mathcal {S} and I \mathcal {I} are reflexive proper linear subspaces of operators acting on a separable Hilbert space, then the hyperreflexivity constant of ( S ⊥ ⊗ I ⊥ ) ⊥ {({\mathcal {S}_ \bot } \otimes {\mathcal {I}_ \bot })^ \bot } is at least as great as the product of the constants of S \mathcal {S} and I \mathcal {I} .