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April 2003 Noncommutative Burkholder/Rosenthal inequalities
Marius Junge, Quanhua Xu
Ann. Probab. 31(2): 948-995 (April 2003). DOI: 10.1214/aop/1048516542

Abstract

We investigate martingale inequalities in noncommutative $L^p$-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.

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Marius Junge. Quanhua Xu. "Noncommutative Burkholder/Rosenthal inequalities." Ann. Probab. 31 (2) 948 - 995, April 2003. https://doi.org/10.1214/aop/1048516542

Information

Published: April 2003
First available in Project Euclid: 24 March 2003

zbMATH: 1041.46050
MathSciNet: MR1964955
Digital Object Identifier: 10.1214/aop/1048516542

Subjects:
Primary: 46L53

Keywords: (noncommutative) Burkholder inequality , (Noncommutative) martingale inequalities , (noncommutative) Rosenthal inequality , noncommuntative $L^p$-spaces

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 2 • April 2003
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