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Journal of Operator Theory

Volume 36, Issue 1, Summer 1996  pp. 21-43.

Preannihilators, the operator approximation property and dual products

Authors: Jon Kraus 1 and David R. Larson 2
Author institution:1 Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14214, U.S.A.
2 Department of Mathematics, Texas A & M University, College Station, TX 77843, U.S.A.


Summary: It was shown by Effros, Kraus and Ruan that an ultraweakly closed subspace of BH has the weak*-operator approximation property if and only if its predual has the operator approximation property. We show that the preannihilator of such a subspace S has the operator approximation property if and only if any ultraweakly closed subspace T of BK the dual product of S and T is the ultraweakly closed linear span of the algebraic tensor product of S and BK and the algebraic tensor product of BH and T. Using this we also show that there are reflexive subspaces S and T for which the dual product is strictly larger than this ultraweakly closed linear span, answering a question of the second author.

Keywords: Operator space, tensor product, dual product, hyperreflexive, operator approximation property, preannihilator.


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