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The structure of mean equicontinuous group actions

Fuhrmann, Gabriel and Gröger, Maik and Lenz, Daniel (2022) 'The structure of mean equicontinuous group actions.', Israel Journal of Mathematics, 247 . pp. 75-123.

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.

Item Type:Article
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution 4.0.
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Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution 4.0.
Download PDF
(472Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s11856-022-2292-8
Publisher statement: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.
Date accepted:No date available
Date deposited:13 May 2022
Date of first online publication:06 March 2022
Date first made open access:13 May 2022

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