Failure of almost uniform convergence for noncommutative martingales

被引：0
|
作者：
Hong, Guixiang [1 ]
Ricard, Eric [2 ]
机构：
[1] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China
[2] UNICAEN, CNRS, LMNO, F-14000 Caen, France
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2024年
基金：
中国国家自然科学基金;
关键词：
Almost uniform convergence; Bilateral almost uniform convergence; Noncommutative L-p-spaces; ERGODIC-THEOREMS;
D O I：
10.1007/s00440-024-01300-5
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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 <= 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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页数：10
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