Lp-matricially normed spaces and operator space valued schatten spaces

Marius Junge; Christian Le Merdy; Lahcène Mezrag

doi:10.1512/iumj.2007.56.3070

L^p-matricially normed spaces and operator space valued schatten spaces

Marius Junge, Christian Le Merdy, Lahcène Mezrag

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let 1 ≤ p < ∞ and let F be an operator space. Let S _k^p [F] be Pisier's operator space valued Schatten space, for any integer k ≥ 1. Then F equipped with the matrix norms given by the S_k^p[F]'s is an L^p-matricially normed space. We show that if p ≠ 1, not all L^p-matricially normed spaces are of this form. Then we give a characterization of those L^p-matricially normed spaces which are of this form. Indiana University Mathematics Journal

Original language	English (US)
Pages (from-to)	2511-2534
Number of pages	24
Journal	Indiana University Mathematics Journal
Volume	56
Issue number	5
DOIs	https://doi.org/10.1512/iumj.2007.56.3070
State	Published - 2007

Keywords

Completely bounded maps
L-matricially normed spaces
Operator spaces

ASJC Scopus subject areas

General Mathematics

Online availability

10.1512/iumj.2007.56.3070

Library availability

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Cite this

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abstract = "Let 1 ≤ p < ∞ and let F be an operator space. Let S kp [F] be Pisier's operator space valued Schatten space, for any integer k ≥ 1. Then F equipped with the matrix norms given by the Skp[F]'s is an Lp-matricially normed space. We show that if p ≠ 1, not all Lp-matricially normed spaces are of this form. Then we give a characterization of those Lp-matricially normed spaces which are of this form. Indiana University Mathematics Journal",

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