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A Maurey type result for operator spaces

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arxiv 0707.0152 v2 pith:OKLHPVW2 submitted 2007-07-02 math.FA math.OA

A Maurey type result for operator spaces

classification math.FA math.OA
keywords operatoreverysumminganaloguecb-mapmaureyspacespaces
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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 $\|v(x)\| \leq c(q) \|v\|_{cb} \|axb\|_q$ with $a,b$ in the unit ball of the Schatten class $S_{2q}$.

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