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.
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This work was partially supported by the National Natural Science Foundation of China (11001273,90820302), the Fundamental Research Funds for the Central Universities (2010QYZD001), Research Fund for the Doctoral Program of Higher Education of China (20100162120035) and Postdoctoral Science Foundation of China and Central South University.
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Jiao, Y. Martingale inequalities in noncommutative symmetric spaces. Arch. Math. 98, 87–97 (2012). https://doi.org/10.1007/s00013-011-0343-1
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DOI: https://doi.org/10.1007/s00013-011-0343-1