- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- Convergence and Gundy's decomposition for noncommutative quasi-martingales
Convergence and Gundy's decomposition for noncommutative quasi-martingales
Authors : Congbian Ma, Ping Li, Youliang Hou
Pages : 2724-2734
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Publication Date : 9999-12-31
Article Type : Makaleler
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