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arXiv · 2402.08560

Failure of almost uniformly convergence for noncommutative martingales

Guixiang Hong·Éric Ricard
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Abstract

In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative $L_p$-martingales when $1\leq p<2$. The same happens to ergodic averages. The proof consists of some sharp estimates of the distributional function of a sequence of matrices and some non standard transference techniques, which might admit further applications.

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Guixiang Hong, Éric Ricard. 2024-02-13. Failure of almost uniformly convergence for noncommutative martingales. https://arxiv.org/abs/2402.08560

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