A Maurey type result for operator spaces

Marius Junge, Hun Hee Lee

Research output: Contribution to journalArticlepeer-review

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 [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 {norm of matrix} v (x) {norm of matrix} ≤ c (q) {norm of matrix} v {norm of matrix}cb {norm of matrix} a x b {norm of matrix}q with a, b in the unit ball of the Schatten class S2 q.

Original languageEnglish (US)
Pages (from-to)1373-1409
Number of pages37
JournalJournal of Functional Analysis
Volume254
Issue number5
DOIs
StatePublished - Mar 1 2008

Keywords

  • Completely p-summing map
  • Operator Hilbert space
  • Operator space

ASJC Scopus subject areas

  • Analysis

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