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Some classes of multilinear operators on C(K) spaces

Fernando Bombal;  Maite Fernández;  Ignacio Villanueva — 2001

Studia Mathematica

We obtain a classification of projective tensor products of C(K) spaces according to whether none, exactly one or more than one factor contains copies of ℓ₁, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces or the verification of certain Banach space properties of the corresponding tensor product. The main tool is an improvement of some results of Emmanuele and Hensgen on the reciprocal Dunford-Pettis and Pełczyński's (V) properties of the projective...

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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