2020/09/24 by Sayan Das, Das, Sayan, Jesse Peterson +1 · 1 citation
Mathematics · #46L10 #46L55 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2009.11787
openalex publication_date 2020/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce Poisson boundaries of II1 factors with respect to density operators that give the traces. The Poisson boundary is a von Neumann algebra that contains the II1 factor and is a particular example of the boundary of a unital completely positive map as introduced by Izumi. Studying the inclusion of the II1 factor into its boundary we develop a number of notions, such as double ergodicity and entropy, that can be seen as natural analogues of results regarding the Poisson boundaries introduced by Furstenberg. We use the techniques developed to answer a problem of Popa by showing that all finite factors satisfy the MV-property. We also extend a result of Nevo by showing that property (T) factors give rise to an entropy gap.