Biduals of tensor products in operator spaces
Tom 230 / 2015
Studia Mathematica 230 (2015), 165-185
MSC: Primary 47L25; Secondary 46M05, 47L22.
DOI: 10.4064/sm8292-1-2016
Opublikowany online: 4 February 2016
Streszczenie
We study whether the operator space ${{V^{**}\overset\alpha\otimes W^{**}}}$ can be identified with a subspace of the bidual space ${(V\overset\alpha\otimes W)^{**}}$, for a given operator space tensor norm. We prove that this can be done if $\alpha$ is finitely generated and $V$ and $W$ are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When $\alpha$ is the projective, Haagerup or injective norm, the hypotheses can be weakened.
