Noncommutative Poisson boundaries, ultraproducts and entropy
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913211923562496 |
|---|---|
| author | Zhou, Shuoxing |
| author_facet | Zhou, Shuoxing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12763 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Noncommutative Poisson boundaries, ultraproducts and entropy Zhou, Shuoxing Operator Algebras Dynamical Systems Group Theory 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. |
| title | Noncommutative Poisson boundaries, ultraproducts and entropy |
| topic | Operator Algebras Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2306.12763 |