Maximal theorems of Menchoff-Rademacher type in non-commutative Lq-spaces

Andreas Defant, Marius Junge

Research output: Contribution to journalArticlepeer-review

Abstract

Estimates for maximal functions provide the fundamental tool for solving problems on pointwise convergence. This applies in particular for the Menchoff-Rademacher theorem on orthogonal series in L2[0, 1] and for results due independently to Bennett and Maurey-Nahoum on unconditionally convergent series in L1 [0, 1]. We prove corresponding maximal inequalities in non-commutative Lq-spaces over a semifinite von Neumann algebra. The appropriate formulation for non-commutative maximal functions originates in Pisier's recent work on non-commutative vector valued Lq-spaces.

Original languageEnglish (US)
Pages (from-to)322-355
Number of pages34
JournalJournal of Functional Analysis
Volume206
Issue number2
DOIs
StatePublished - Jan 15 2004

Keywords

  • Maximal function
  • Non-communitative L-spaces
  • Unconditional sequences

ASJC Scopus subject areas

  • Analysis

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