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Archiv der Mathematik

, Volume 98, Issue 1, pp 87–97 | Cite as

Martingale inequalities in noncommutative symmetric spaces

  • Yong Jiao
Article

Abstract

We investigate the Burkholder–Gundy inequalities in a noncommutative symmetric space \({E(\mathcal{M})}\) associated with a von Neumann algebra \({\mathcal{M}}\) equipped with a faithful normal state. The results extend the Pisier–Xu noncommutative martingale inequalities, and generalize the classical inequalities in the commutative case.

Mathematics Subject Classification (2010)

Primary 46L53 Secondary 60G42 

Keywords

Noncommutative martingale Burkholder–Gundy’s inequalities Symmetric operator spaces 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Institute of Probability and StatisticsCentral South UniversityChangshaChina

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