Amenability and subexponential spectral growth rate of Dirichlet forms on von Neumann algebras

Published 6 Nov 2016 in math.OA | (1611.01749v3)

Abstract: In this work we apply Noncommutative Potential Theory to prove (relative) amenability and the (relative) Haagerup Property $(H)$ of von Neumann algebras in terms of the spectral growth of Dirichlet forms. Examples deal with (inclusions of) countable discrete groups and free orthogonal compact quantum groups.

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