Convergence and Gundy's decomposition for noncommutative quasi-martingales

Authors: CONGBIAN MA, PING LI, YOULIANG HOU

Abstract: In this paper, we prove the bilaterally almost uniformly convergence of bounded $L_1(\mathcal{M})$-noncommutative quasi-martingales. We also prove Gundy's decomposition for noncommutative quasi-martingales. As an application, we prove that every relatively weakly compact quasi-martingale difference sequence in $L_1(\mathcal{M},\tau)$ whose sequence of norms is bounded away from zero is 2-co-lacunary.

Keywords: Convergence, Gundy's decomposition, noncommutative quasi-martingales

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