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

## TL;DR

This paper characterizes the primitive ideal space of the partial-isometric crossed product of a $C^*$-algebra by a single automorphism, using its realization as a full corner of a classical crossed product.

## Contribution

It provides a detailed description of the primitive ideal space for the partial-isometric crossed product via realization as a full corner, extending understanding of such structures.

## Key findings

- Primitive ideal space described explicitly
- Realization as a full corner used in analysis
- Connections to classical crossed product theory

## 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 $A\times_{\alpha}^{\textrm{piso}}\mathbb{N}$ of the system by using its realization as a full corner of a classical crossed product and applying some results of Williams and Echterhoff.