Banach algebra dynamical systems

Abstract

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 ⋊_α G coincides with ⋊_α,r G.

Keywords

Banach algebra dynamical systems / Representation / Crossed product / Left multiplier / Reduced crossed product

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