Hyperreflexivity and a dual product construction Academic Article

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} .