Biduals of tensor products in operator spaces

Verónica Dimant, and Maite Fernández-Unzueta. "Biduals of tensor products in operator spaces." Studia Mathematica 230.2 (2015): 165-185. <http://eudml.org/doc/285414>.

@article{VerónicaDimant2015,
abstract = {We study whether the operator space $V** \overset\{α\}\{⊗\} W**$ can be identified with a subspace of the bidual space $(V \overset\{α\}\{⊗\} W)**$, 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.},
author = {Verónica Dimant, Maite Fernández-Unzueta},
journal = {Studia Mathematica},
keywords = {operator spaces; tensor products; bilinear mappings},
language = {eng},
number = {2},
pages = {165-185},
title = {Biduals of tensor products in operator spaces},
url = {http://eudml.org/doc/285414},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Verónica Dimant
AU - Maite Fernández-Unzueta
TI - Biduals of tensor products in operator spaces
JO - Studia Mathematica
PY - 2015
VL - 230
IS - 2
SP - 165
EP - 185
AB - We study whether the operator space $V** \overset{α}{⊗} W**$ can be identified with a subspace of the bidual space $(V \overset{α}{⊗} W)**$, 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.
LA - eng
KW - operator spaces; tensor products; bilinear mappings
UR - http://eudml.org/doc/285414
ER -