Dilations and rigid factorisations on noncommutative Lp-spaces

Marius Junge, Christian Le Merdy

Research output: Contribution to journalArticlepeer-review

Abstract

We study some factorisation and dilation properties of completely positive maps on noncommutative Lp-spaces. We show that Akcoglu's dilation theorem for positive contractions on classical (= commutative) Lp-spaces has no reasonable analog in the noncommutative setting. Our study relies on nonsymmetric analogs of Pisier's operator space valued noncommutative Lp-spaces that we investigate in the first part of the paper.

Original languageEnglish (US)
Pages (from-to)220-252
Number of pages33
JournalJournal of Functional Analysis
Volume249
Issue number1
DOIs
StatePublished - Aug 1 2007

Keywords

  • Completely positive maps
  • Dilations
  • Noncommutative L-spaces
  • Operator spaces

ASJC Scopus subject areas

  • Analysis

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