A reduction method for noncommutative Lp-Spaces and applications

Uffe Haagerup, Marius Junge, Quanhua Xu

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the reduction of problems on general noncommuta- tive L p-spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is an unpublished result of the first-named author which approximates any noncommutative Lp-space by tracial ones. We show that under some natural conditions a map between two von Neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative Lp-spaces. We present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale/ergodic inequalities to those in the tracial case.

Original languageEnglish (US)
Pages (from-to)2125-2165
Number of pages41
JournalTransactions of the American Mathematical Society
Volume362
Issue number4
DOIs
StatePublished - Apr 2010

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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