数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 729-752.doi: 10.1007/s10473-021-0307-x

• 论文 • 上一篇    下一篇

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

连媛1, 黄小军1,2, 李智强1   

  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
  • 收稿日期:2019-11-06 修回日期:2020-08-20 出版日期:2021-06-25 发布日期:2021-06-07
  • 通讯作者: Xiaojun HUANG E-mail:hxj@cqu.edu.cn
  • 作者简介:Yuan LIAN,E-mail:20140602035@cqu.edu.cn;Zhiqiang LI,E-mail:zqli@cqu.edu.cn
  • 基金资助:
    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).

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).

摘要: 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.

关键词: Proximal relation, amenable group, mean equicontinuity

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

中图分类号: 

  • 37A35