The structure of mean equicontinuous group actions

Fuhrmann, Gabriel; Gröger, Maik; Lenz, Daniel

doi:10.1007/s11856-022-2292-8

The structure of mean equicontinuous group actions

Fuhrmann, Gabriel; Gröger, Maik; Lenz, Daniel

Authors

Dr Gabriel Fuhrmann gabriel.fuhrmann@durham.ac.uk
Assistant Professor

Maik Gröger

Daniel Lenz

Abstract

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.

Citation

Fuhrmann, G., Gröger, M., & Lenz, D. (2022). The structure of mean equicontinuous group actions. Israel Journal of Mathematics, 247, 75-123. https://doi.org/10.1007/s11856-022-2292-8

Journal Article Type	Article
Online Publication Date	Mar 6, 2022
Publication Date	2022
Deposit Date	May 13, 2022
Publicly Available Date	May 13, 2022
Journal	Israel Journal of Mathematics
Print ISSN	0021-2172
Electronic ISSN	1565-8511
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	247
Pages	75-123
DOI	https://doi.org/10.1007/s11856-022-2292-8

Files

Published Journal Article (Advance online version) (471 Kb)
PDF

Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Advance online version Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.