Abstract
Let $(A,\mathbb{N}^{2},\alpha)$ be a dynamical system consisting of a $C^{*}$-algebra $A$ and an action $\alpha$ of $\mathbb{N}^{2}$ on $A$ by automorphisms. Let $A \times_{\alpha}^{\mathrm{piso}} \mathbb{N}^{2}$ be the partial-isometric crossed product of the system. We apply the fact that it is a full corner of a crossed product by the group $\mathbb{Z}^{2}$ in order to give a complete description of its primitive ideal space.
Funding Statement
This work (Grant No. RGNS 64-102) was financially supported by Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation, Thailand.
Acknowledgments
The author would like to thank the anonymous reviewer for valuable suggestions and comments to improve the earlier version of the paper.
Citation
Saeid Zahmatkesh. "The Primitive Ideal Space of the Partial-isometric Crossed Product by Automorphic Actions of the Semigroup $\mathbb{N}^{2}$." Taiwanese J. Math. Advance Publication 1 - 24, 2024. https://doi.org/10.11650/tjm/231205
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