Maurey’s factorization theory for operator spaces
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- Junge, M. & Parcet, J. Math. Ann. (2010) 347: 299. doi:10.1007/s00208-009-0440-7
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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 VN(G) associated with a discrete group G. We also develop a notion of cotype which is compatible with factorization results on noncommutative Lp spaces.