An approach to the study of boundary actions
Abstract
Given an action of a discrete countable group $G$ on a countable set $\mathfrak{X}$, it is studied the relationship between properties of the associated Calkin representation and the dynamics of the group action on the boundary of the StoneČech compactification of $\mathfrak{X}$. The first section contains results about amenability properties of actions of discrete countable groups on nonseparable 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 C}ech boundary within the common framework of measurable dynamics on certain extensions of the Stone{\v C}ech boundary of $\mathfrak{X}$.
 Publication:

arXiv eprints
 Pub Date:
 May 2023
 DOI:
 10.48550/arXiv.2305.16277
 arXiv:
 arXiv:2305.16277
 Bibcode:
 2023arXiv230516277B
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Dynamical Systems;
 Mathematics  Group Theory;
 46L05
 EPrint:
 Minor corrections