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Biduals of tensor products in operator spaces

Volume 230 / 2015

Verónica Dimant, Maite Fernández-Unzueta Studia Mathematica 230 (2015), 165-185 MSC: Primary 47L25; Secondary 46M05, 47L22. DOI: 10.4064/sm8292-1-2016 Published online: 4 February 2016

Abstract

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.

Authors

  • Verónica DimantDepartamento de Matemática
    Universidad de San Andrés
    Vito Dumas 284
    (B1644BID) Victoria
    Buenos Aires, Argentina
    and
    CONICET
    e-mail
  • Maite Fernández-UnzuetaCentro de Investigación en Matemáticas (Cimat)
    A.P. 402
    Guanajuato, Gto., México
    e-mail

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