Maurey's factorization theory for operator spaces

Marius Junge, Javier Parcet

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)299-338
Number of pages40
JournalMathematische Annalen
Volume347
Issue number2
DOIs
StatePublished - 2010

ASJC Scopus subject areas

  • Mathematics(all)

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