Noncommutative Burkholder/Rosenthal inequalities

Abstract

We investigate martingale inequalities in noncommutative Lp-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.