A Maurey type result for operator spaces

2007/07/02 by Marius Junge, Junge, Marius, Hun Hee Lee +1
Mathematics · #46B07 #47L25 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46B07 #msc:47L25

paper · pdf · doi:10.48550/arxiv.0707.0152

29 pages. To appear in Journal of Functional Analysis

arxiv created 2007/11/08 · arxiv updated 2009/12/01

Abstract

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 \citeJ05 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 S_2q.

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