Noncommutative Joinings II

2019/05/16 by Bannon, Jon, Cameron, Jan, Mukherjee, Kunal
#37A55 #46L10 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1905.06725

Abstract

This paper is a continuation of the authors' previous work on noncommutative joinings, and contains a study of relative independence of W^*-dynamical systems. We prove that, given any separable locally compact group G, an ergodic W^*-dynamical G-system \mathfrakM with compact subsystem \mathfrakN is disjoint relative to \mathfrakN from its maximal compact subsystem \mathfrakM_K if and only if \mathfrakN≅\mathfrakM_K. This generalizes recent work of Duvenhage, which established the result for G abelian.

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