Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 729-752.doi: 10.1007/s10473-021-0307-x

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THE PROXIMAL RELATION, REGIONALLY PROXIMAL RELATION AND BANACH PROXIMAL RELATION FOR AMENABLE GROUP ACTIONS

Yuan LIAN1, Xiaojun HUANG1,2, Zhiqiang LI1   

  1. 1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
    2. Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing 401331, China
  • Received:2019-11-06 Revised:2020-08-20 Online:2021-06-25 Published:2021-06-07
  • Contact: Xiaojun HUANG E-mail:hxj@cqu.edu.cn
  • About author:Yuan LIAN,E-mail:20140602035@cqu.edu.cn;Zhiqiang LI,E-mail:zqli@cqu.edu.cn
  • Supported by:
    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).

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.

Key words: Proximal relation, amenable group, mean equicontinuity

CLC Number: 

  • 37A35
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