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 $\{\mathbf{1}_{gHg^{-1}}\}_{g\in G}$ 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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Topology and Set Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 February 2026
- Language
- EN
- Document type
- Preprint