Ideals with approximate unit in semicrossed products

Abstract

Abstract We characterize the ideals of the semicrossed product $C_0(X)\times _\phi {\mathbb Z}_+$ , associated with suitable sequences of closed subsets of X , with left (resp. right) approximate unit. As a consequence, we obtain a complete characterization of ideals with left (resp. right) approximate unit under the assumptions that X is metrizable and the dynamical system $(X,\phi )$ contains no periodic points.