# Caractérisation Des Espaces 1-Matriciellement Normés

Le Merdy, Christian; Mezrag, Lahcéne

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 3, page 201-206
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topLe 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.