Noncommutative Burkholder/Rosenthal inequalities

Marius Junge, Quanhua Xu

Research output: Contribution to journalArticlepeer-review


We investigate martingale inequalities in noncommutative Lp-spaces associated with a von Neumann algebra equipped with a faithful normal state. We prove the noncommutative analogue of the classical Burkholder inequality on the conditioned (or little) square function and extend the noncommutative Burkholder-Gundy inequalities from Comm. Math. Phys. 189 (1997) 667-698 to this nontracial setting. We include several related results.

Original languageEnglish (US)
Pages (from-to)948-995
Number of pages48
JournalAnnals of Probability
Issue number2
StatePublished - Apr 2003


  • (Noncommutative) martingale inequalities
  • (noncommutative) Burkholder inequality
  • (noncommutative) Rosenthal inequality
  • Noncommutative L spaces

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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