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Title page for ETD etd-07202017-142037


Type of Document Dissertation
Author Das, Sayan
Author's Email Address sayan.das@vanderbilt.edu
URN etd-07202017-142037
Title Poisson boundaries of finite von Neumann algebras
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Jesse D. Peterson Committee Chair
Vaughan Jones Committee Co-Chair
Akram Aldroubi Committee Member
Dietmar Bisch Committee Member
Robert J. Scherrer Committee Member
Keywords
  • property (T)
  • amenability
  • hyperstate
  • entropy
  • rigidity
  • operator systems
Date of Defense 2017-04-19
Availability unrestricted
Abstract
Poisson boundaries of groups plays a major role in the study of group actions on measure spaces. In this work, we study noncommmutative Poisson boundaries of finite von Neumannalgebras. We prove a noncommutative analogue of the double ergodicity theorem due to V.Kaimanovich and give applications to the study of derivations on a finite von Neumann algebra,and the similarity problem. We also prove a boundary rigidity theorem, using double ergodicity. We also define and study the notions of noncommutative Avez entropy, and noncommutative Fustenberg entropy, and show an entropy gap theorem for von Neumann algebras with property(T).
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