Noncommutative Poisson Boundaries, Ultraproducts, and Entropy

被引：2
|
作者：
Zhou, Shuoxing [1 ,2 ]
机构：
[1] Ecole Normale Super, Dept Math & Applicat, F-75005 Paris, France
[2] Univ Paris Saclay, Lab Math Orsay, F-91405 Orsay, France
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 10期
关键词：
MAPS;
D O I：
10.1093/imrn/rnae022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct the noncommutative Poisson boundaries of tracial von Neumann algebras through the ultraproducts of von Neumann algebras. As an application of this result, we complete the proof of Kaimanovich-Vershik's fundamental theorems regarding noncommutative entropy. We also prove the Amenability-Trivial Boundary equivalence and Choquet-Deny-Type I equivalence for tracial von Neumann algebras.
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页码：8794 / 8818
页数：25
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