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Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

We study whether the operator space V * * α W * * can be identified with a subspace of the bidual space ( V α W ) * * , for a given operator space tensor norm. We prove that this can be done if α 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 α is the projective, Haagerup or injective norm, the hypotheses can be weakened.

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