Noncommutative Burkholder/Rosenthal inequalities
Marius Junge and Quanhua Xu
Source: Ann. Probab. Volume 31, Number 2 (2003), 948-995.
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.
Primary Subjects: 46L53
Keywords: (Noncommutative) martingale inequalities; noncommuntative $L^p$-spaces; (noncommutative) Burkholder inequality; (noncommutative) Rosenthal inequality
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1048516542
Digital Object Identifier: doi:10.1214/aop/1048516542
Mathematical Reviews number (MathSciNet):
MR1964955
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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
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