, Volume 347, Issue 2, pp 299-338
Date: 29 Oct 2009

Maurey’s factorization theory for operator spaces

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Abstract

We prove an operator space version of Maurey’s theorem, which claims that every absolutely (p, 1)-summing map on C(K) is automatically absolutely q-summing for q > p. Our results imply in particular that every completely bounded map from B(H) with values in Pisier’s operator space OH is completely p-summing for p > 2. This fails for p = 2. As applications, we obtain eigenvalue estimates for translation invariant maps defined on the von Neumann algebra V N(G) associated with a discrete group G. We also develop a notion of cotype which is compatible with factorization results on noncommutative L p spaces.