A Maurey type result for operator spaces

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and 2 is 2-summing. However, it is shown in [M. Junge, Embedding of the operator space OH and the logarithmic ‘little Grothendieck inequality’, Invent. Math. 161 (2) (2005) 225–286] that the operator space analogue fails. Not every cb-map v :K → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey’s theorem: every cb-map v :K→OH is (q, cb)-summing for any q >2 and hence admits a factorization v(x) c(q) v cb axb q with a, b in the unit ball of the Schatten class S2q . © 2007 Elsevier Inc. All rights reserved.