Pro-Banach代数动力系统（英文）  

Pro-Banach Algebra Dynamical Systems

作　　者：黄利忠[1] HUANG Lizhong(Institute of Quantum Information Science,Shanxi Datong University,Datong,Shanxi,037009,P.R.China)

机构地区：[1]山西大同大学量子信息科学研究所,大同山西037009

出　　处：《数学进展》2018年第6期923-933,共11页Advances in Mathematics（China）

基　　金：supported by NSFC(Nos.11571247,11301312);the Science Technology Plan Project of Datong City(No.2018151);the Doctoral Scientific Research Foundation of Shanxi Datong University(No.2015-B-09)

摘　　要：本文将Banach代数动力系统的概念推广到pro-Banach代数动力系统,证明了当动力系统(A,G,α)可逆时,L^1(G,A,α)_p是一族空间L^1(G,A_p,α^((p)))(p∈m(A))的逆极限.最后,本文证明了在一定的条件下,(A,G,α)在Banach空间上的非退化连续共变表示与L^1(G,A,α)在相同Banach空间上的非退化连续表示是一一对应的.This paper generalizes the concept of Banach algebra dynamical system to pro-Banach algebra dynamical system, and shows that when （A, G, α） is inverse, L1 （G, A, α）p is an inverse limit of a family of LI（G, Ap, α（P）） for all p ∈ re（A）. Finally, we prove that the non-degenerate continuous covariant representations of （A, G, α） on a Banach space are bijective with non-degenerate continuous representations of L1 （G, A, α） on the same Banach space under some conditions.

关 键 词：pro—Banach代数动力系统 同构 表示 

分 类 号：O177.5[理学—数学]