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Biduals of tensor products in operator spaces

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Dimant V., Fernández-Unzueta M.

Studia Mathematica

2015

tom 230

nr 2

165-185

We study whether the operator space $V** \overset{α}{⊗} W**$ can be identified with a subspace of the bidual space $(V \overset{α}{⊗} W)**$, 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.

Ograniczanie wyników

1 Studia Mathematica

1 Dimant V.

1 Fernández-Unzueta M.

1 2015

Wyniki wyszukiwania

Biduals of tensor products in operator spaces