Noncommutative Burkholder/Rosenthal inequalities

• Marius Junge ^[1] ; Quanhua Xu ^[2]
  1. [1] University of Illinois
  2. [2] Université de Franche-Conté
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 2, 2003, págs. 948-995
• Idioma: inglés
• DOI: 10.1214/aop/1048516542
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• Resumen

  • 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.