The structure of mean equicontinuous group actions

Fuhrmann, Gabriel; Gröger, Maik; Lenz, Daniel

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
• Public URL: https://durham-repository.worktribe.com/output/1207493