Geodesic
Biduals of tensor products in operator spaces
Verónica Dimant1 ; Maite Fernández-Unzueta2
1 Departamento de Matemática Universidad de San Andrés Vito Dumas 284 (B1644BID) Victoria Buenos Aires, Argentina and CONICET
2 Centro de Investigación en Matemáticas (Cimat) A.P. 402 Guanajuato, Gto., México
Studia Mathematica, Tome 230 (2015) no. 2, pp. 165-185

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
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

Verónica Dimant 1 ; Maite Fernández-Unzueta 2

1 Departamento de Matemática Universidad de San Andrés Vito Dumas 284 (B1644BID) Victoria Buenos Aires, Argentina and CONICET
2 Centro de Investigación en Matemáticas (Cimat) A.P. 402 Guanajuato, Gto., México 
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Verónica Dimant; Maite Fernández-Unzueta. Biduals of tensor products in operator spaces. Studia Mathematica, Tome 230 (2015) no. 2, pp. 165-185. doi: 10.4064/sm8292-1-2016

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