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arXiv · 2602.14176

Conjugacy co-amenability

Mehrdad Kalantar·Srivatsav Kunnawalkam Elayavalli
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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 $\{\mathbf{1}_{gHg^{-1}}\}_{g\in G}$ viewed inside $\ell^\infty(G)$. 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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Mehrdad Kalantar, Srivatsav Kunnawalkam Elayavalli. 2026-02-15. Conjugacy co-amenability. https://arxiv.org/abs/2602.14176

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