Doob's inequality for non-commutative martingales
M. Junge
Abstract
Let 1 p<\8 and (xn) be a sequence of positive elements in a non-commutative Lp space and (En) be an increasing sequence of conditional expectations, then the Lp norm of Σn En(xn) can be estimated by cp times the Lp norm of Σn xn. This inequality is due to Burkholder, Davis and Gundy in the commutative case. By duality, we obtain a version of Doob's maximal inequality for 1<p \8.
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