Failure of almost uniform convergence for noncommutative martingales
Guixiang Hong 洪桂祥 (Harbin Institute of Technology)
14:00-15:00, November 27, 2024 Science Building A503
Abstract:
In this talk, I shall present the joint work with Eric Ricard, which asserts that the almost uniform convergence may not happen for truly noncommutative Lp -martingales when 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.
About the speaker:
洪桂祥，哈尔滨工业大学教授，2016年入选国家高层次人才青年计划，2023年获批国家杰出青年科学基金项目。他专注于调和分析、非交换分析及其在非交换几何和量子信息中的应用，为这一前沿领域的建立和发展做出重要贡献，已在《Duke Mathematical Journal》《Memoirs of the American Mathematical Society》《Advances in Mathematics》等顶级期刊发表论文30余篇。其研究方向涵盖经典与非交换调和分析、量子概率论、非交换遍历理论和泛函分析，尤其在非交换鞅论、非交换遍历论等方面取得突破，解决了若干公开问题。
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