Noncommutative Poisson boundaries, ultraproducts and entropy
Operator Algebras
2024-01-30 v3 Dynamical Systems
Group Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2306.12763,
title = {Noncommutative Poisson boundaries, ultraproducts and entropy},
author = {Shuoxing Zhou},
journal= {arXiv preprint arXiv:2306.12763},
year = {2024}
}
Comments
Remark 5.7 has been added to show Choquet-Deny property of groups can not be perfectly extended to tracial von Neumann algebras