The primitive ideal space of the partial-isometric crossed product of a system by a single automorphism

Abstract

Let $(A,\alpha )$ be a system consisting of a $C^*$-algebra $A$ and an automorphism $\alpha $ of~$A$. We describe the primitive ideal space of the partial-isometric crossed product $A\times _{\alpha }^{piso }\mathbb{N} $ of the system by using its realization as a full corner of a classical crossed product and applying some results of Williams and Echterhoff.