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