The structure of mean equicontinuous group actions

Bibliographic description

punktacja MEiN [2022]: 100

title:	The structure of mean equicontinuous group actions
author:	Fuhrmann Gabriel, Gröger Maik , Lenz Daniel
journal title:	Israel Journal of Mathematics
volume:	247
date of publication :	2022
pages:	75-123
ISSN:	0021-2172
eISSN:	1565-8511
DOI:	10.1007/s11856-022-2292-8
language:	English
journal language:	English
abstract in English:	We study mean equicontinuous actions of locally compact σ-compact amenable groups on compact metric spaces. In this setting, we establish the equivalence of mean equicontinuity and topo-isomorphy to the maximal equicontinuous factor and provide a characterization of mean equicontinuity of an action via properties of its product. This characterization enables us to show the equivalence of mean equicontinuity and the weaker notion of Besicovitch-mean equicontinuity in fairly high generality, including actions of abelian groups as well as minimal actions of general groups. In the minimal case, we further conclude that mean equicontinuity is equivalent to discrete spectrum with continuous eigenfunctions. Applications of our results yield a new class of non-abelian mean equicontinuous examples as well as a characterization of those extensions of mean equicontinuous actions which are still mean equicontinuous.
affiliation:	Wydział Matematyki i Informatyki : Instytut Matematyki
type:	journal article
subtype:	academic paper