Conjugacy co-amenability
Abstract
In this note we study a natural analytic property of inclusions of groups akin to co-amenability: the property of existence of a non-compactly supported invariant state for the conjugation action of a group G on the von Neumann algebra generated by the characteristic functions \1gHg-1\g∈ G viewed inside ∞(G). Some interesting settings and examples of this phenomena are proved. We also comment on a consideration related to proper proximality, which motivated this property.
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