A Maurey type result for operator spaces

Original · EN

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and ℓ₂ is 2-summing. However, it is shown in J05 that the operator space analogue fails. Not every cb-map v: → OH is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem: Every cb-map v: → OH is (q,cb)-summing for any q>2 and hence admits a factorization v(x) ≤ c(q) vcb axbq with a,b in the unit ball of the Schatten class S₂q.