IUMJ

Title: $L^p$-matricially normed spaces and operator space valued Schatten spaces

Authors: Marius Junge, Christian le Merdy and Lahcene Mezrag

Issue: Volume 56 (2007), Issue 5, 2511-2534

Abstract:

Let $1 \leq p < \infty$ and let $F$ be an operator space. Let $S^p_k[F]$ be Pisier's operator space valued Schatten space, for any integer $k \geq 1$. Then $F$ equipped with the matrix norms given by the $S^p_k[F]$'s is an $L^p$-matricially normed space. We show that if $p \not= 1$, 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.