摘要
This paper generalizes the C*-dynamical system to the Banach algebra dynamical system(A,G,α)and define the crossed product A α G of a given Banach algebra dynamical system(A,G,α).Then the representation of A α G is described when A admits a bounded left approximate identity.In a natural way,the authors define the reduced crossed product A α,r G and discuss the question when A α G coincides with A α,r G.
Abstract This paper generalizes the C＊-dynamical system to the Banach algebra dynam- ical system （A, G, α） and define the crossed product A αG of a given Banach algebra dynamical system （A, G,α）. Then the representation of A α G is described when A ad- mits a bounded left approximate identity. In a natural way, the authors define the reduced crossed product A αG and discuss the question when A α G coincides with A αG.
基金
supported by the National Natural Science Foundation of China(No.10971023)
the Shanghai Natural Science Foundation of China(No.09ZR1402000)
关键词
BANACH代数
动力系统
交叉积
L系统
定义
有界
Banach algebra dynamical systems, Representation, Crossed product, Left multiplier, Reduced crossed product
