A Maurey type result for operator spaces

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between $C(K)$ and ${\mathrm{\ell }}_2$ 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 $v:\text{K}\to OH$ is $(q,cb)$-summing for any $q>2$ and hence admits a factorization $|v(x)| \leq c(q) |v|_{cb} |axb|q$with$a,b$intheunitballoftheSchattenclass$S{2q}$.