## The primitive ideal space of the partial-isometric crossed product of a system by a single automorphism.(English)Zbl 1391.46073

Summary: Let $$(A,\alpha)$$ be a system consisting of a $$C^\ast$$-algebra $$A$$ and an automorphism $$\alpha$$ of $$A$$. We describe the primitive ideal space of the partial-isometric crossed product $$A\times_\alpha^{\mathrm{piso}}\mathbb{N}$$ of the system by using its realization as a full corner of a classical crossed product and applying some results of D. P. Williams [Crossed products of $$C$$*-algebras. Providence, RI: American Mathematical Society (AMS) (2007; Zbl 1119.46002)] and S. Echterhoff [“Crossed products, the Mackey-Rieffel-Green machine and applications”, Preprint (2010), arXiv:1006.4975].

### MSC:

 46L55 Noncommutative dynamical systems

Zbl 1119.46002
Full Text: