2023/05/25 by Jacopo Bassi, Bassi, Jacopo · 2 citations
Mathematics · #46L05 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2305.16277
openalex publication_date 2023/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an action of a discrete countable group G on a countable set \mathfrakX, it is studied the relationship between properties of the associated Calkin representation and the dynamics of the group action on the boundary of the Stone-Čech compactification of \mathfrakX. The first section contains results about amenability properties of actions of discrete countable groups on non-separable spaces and is of independent interest. In the second section these results are applied in order to translate regularity properties of the Calkin representation and the topological amenability on the Stone-\v Cech boundary within the common framework of measurable dynamics on certain extensions of the Stone-\v Cech boundary of \mathfrakX.