We study whether the operator space can be identified with a subspace of the bidual space , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8292-1-2016,
author = {Ver\'onica Dimant and Maite Fern\'andez-Unzueta},
title = {Biduals of tensor products in operator spaces},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {165-185},
zbl = {06545403},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8292-1-2016}
}
Verónica Dimant; Maite Fernández-Unzueta. Biduals of tensor products in operator spaces. Studia Mathematica, Tome 231 (2015) pp. 165-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8292-1-2016/