Abstract
In this paper, we study the proximal relation, regionally proximal relation and Banach proximal relation of a topological dynamical system for amenable group actions. A useful tool is the support of a topological dynamical system which is used to study the structure of the Banach proximal relation, and we prove that above three relations all coincide on a Banach mean equicontinuous system generated by an amenable group action.
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Acknowledgements
The authors are very grateful to Prof. Hanfeng Li for his generous sharing of knowledge and his ideas regarding the topic. The authors would also like to thank the anonymous referee for his/her careful reading and helpful suggestions concerning this paper.
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The second author is supported by NSF of China (11671057), NSF of Chongqing (cstc2020jcyj-msxmX0694) and the Fundamental Research Funds for the Central Universities (2018CDQYST0023).
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Lian, Y., Huang, X. & Li, Z. The Proximal Relation, Regionally Proximal Relation and Banach Proximal Relation for Amenable Group Actions. Acta Math Sci 41, 729–752 (2021). https://doi.org/10.1007/s10473-021-0307-x
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DOI: https://doi.org/10.1007/s10473-021-0307-x