定量均值遍历不等式：作用于单一非交换 $L_p$ 空间上的幂有界算子
泛函分析
2023-03-31 v2 动力系统
算子代数
摘要
本文中，我们针对固定非交换 空间（）上两类幂有界算子子类建立了定量均值遍历定理，主要涉及幂有界可逆算子与 Lamperti 压缩。我们处理定量遍历定理的方法是使用非交换平方函数不等式。后者的建立涉及若干新要素，如来自半交换调和分析的针对非光滑核的几乎正交性与 Calderón-Zygmund 论证、所考察算子的来自算子论的延拓性质，以及由 Coifman 和 Weiss 提出的经典转移方法的非交换版本。
引用
@article{arxiv.2301.00186,
title = {Quantitative mean ergodic inequalities: power bounded operators acting on one single noncommutative $L_p$ space},
author = {Guixiang Hong and Wei Liu and Bang Xu},
journal= {arXiv preprint arXiv:2301.00186},
year = {2023}
}
备注
33 pages. Based the feedbacks from colleagues, we incorporate the referee's comments and improve substantially the presentation of the paper. In particular, we delete some arguments that might be known to experts and add Remark 7.5 for another approach to show the isometric extension of positive isometry in the case $1<p<2$