$L^p$-matricially normed spaces and operator space valued Schatten spaces Marius JungeChristian Le MerdyLahcene Mezrag 46L0746B28operator spacescompletely bounded maps$L^p$-matricially normed spaces 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. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3070 10.1512/iumj.2007.56.3070 en Indiana Univ. Math. J. 56 (2007) 2511 - 2534 state-of-the-art mathematics http://iumj.org/access/