A Maurey type result for operator spaces

Abstract

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between $C(K)$ and ${\ell }_2$ is 2-summing. However, it is shown in \cite{J05} that the operator space analogue fails. Not every cb-map $v : \K \to OH$ is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem : Every cb-map $v : \K \to OH$ is $(q,cb)$-summing for any $q>2$ and hence admits a factorization $\Vert v(x)\Vert \le c(q)\Vert v{\Vert }_{cb}\Vert axb{\Vert }_q$ with $a,b$ in the unit ball of the Schatten class $S_{2q}$.

29 pages. To appear in Journal of Functional Analysis

References in corpus (1)

• Type and cotype of operator spaces