The Annals of Probability

Noncommutative Burkholder/Rosenthal inequalities

Marius Junge and Quanhua Xu

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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.

Article information

Source
Ann. Probab. Volume 31, Number 2 (2003), 948-995.

Dates
First available: 24 March 2003

Permanent link to this document
http://projecteuclid.org/euclid.aop/1048516542

Digital Object Identifier
doi:10.1214/aop/1048516542

Mathematical Reviews number (MathSciNet)
MR1964955

Subjects
Primary: 46L53: Noncommutative probability and statistics

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

Citation

Junge, Marius; Xu, Quanhua. Noncommutative Burkholder/Rosenthal inequalities. The Annals of Probability 31 (2003), no. 2, 948--995. doi:10.1214/aop/1048516542. http://projecteuclid.org/euclid.aop/1048516542.


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  • URBANA, ILLINOIS 61801 E-MAIL: junge@math.uiuc.edu WEB: http://www.math.uiuc.edu/ mjunge/ LABORATOIRE DE MATHÉMATIQUES UNIVERSITÉ DE FRANCHE-COMTÉ 25030 BESANÇON CEDEX FRANCE E-MAIL: qx@math.univ-fcomte.fr