Caractérisation Des Espaces 1-Matriciellement Normés

Le Merdy, Christian, and Mezrag, Lahcéne. "Caractérisation Des Espaces 1-Matriciellement Normés." Serdica Mathematical Journal 28.3 (2002): 201-206. <http://eudml.org/doc/11556>.

@article{LeMerdy2002,
abstract = {Let X be a closed subspace of B(H) for some Hilbert space H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] = (S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X) and showed that there are p−matricially normed spaces. In this paper we prove that conversely, if X is a p−matricially normed space with p = 1, then there is an operator structure on X, such that M1,n (X) = S1 [X] where Sn,1 [X] is the finite dimentional version of S1 [X]. For p = 1, we have no answer.},
author = {Le Merdy, Christian, Mezrag, Lahcéne},
journal = {Serdica Mathematical Journal},
keywords = {Espace d’opérateurs; Espace P-Matriciellement Normé; Opérateur Complétement Borné; operator spaces; matricially normed spaces},
language = {fre},
number = {3},
pages = {201-206},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Caractérisation Des Espaces 1-Matriciellement Normés},
url = {http://eudml.org/doc/11556},
volume = {28},
year = {2002},
}

TY - JOUR
AU - Le Merdy, Christian
AU - Mezrag, Lahcéne
TI - Caractérisation Des Espaces 1-Matriciellement Normés
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 3
SP - 201
EP - 206
AB - Let X be a closed subspace of B(H) for some Hilbert space H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] = (S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X) and showed that there are p−matricially normed spaces. In this paper we prove that conversely, if X is a p−matricially normed space with p = 1, then there is an operator structure on X, such that M1,n (X) = S1 [X] where Sn,1 [X] is the finite dimentional version of S1 [X]. For p = 1, we have no answer.
LA - fre
KW - Espace d’opérateurs; Espace P-Matriciellement Normé; Opérateur Complétement Borné; operator spaces; matricially normed spaces
UR - http://eudml.org/doc/11556
ER -