Biduals of tensor products in operator spaces

Verónica Dimant¹ ; Maite Fernández-Unzueta²

¹Departamento de Matemática Universidad de San Andrés Vito Dumas 284 (B1644BID) Victoria Buenos Aires, Argentina and CONICET
²Centro de Investigación en Matemáticas (Cimat) A.P. 402 Guanajuato, Gto., México

Studia Mathematica, Tome 230 (2015) no. 2, pp. 165-185

Résumé

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.

Détail

DOI : 10.4064/sm8292-1-2016

Keywords: study whether operator space ** overset alpha otimes ** identified subspace bidual space overset alpha otimes ** given operator space tensor norm prove done alpha finitely generated and locally reflexive addition dual spaces locally reflexive bidual spaces have completely bounded approximation property identification through complete isomorphism alpha projective haagerup injective norm hypotheses weakened