The ideal structure of some analytic crossed products
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- by Miron Shpigel PDF
- Trans. Amer. Math. Soc. 351 (1999), 2515-2538 Request permission
Abstract:
We study the ideal structure of a class of some analytic crossed products. For an $r$-discrete, principal, minimal groupoid $G$, we consider the analytic crossed product $C^*(G,\sigma )\times _\alpha \mathbb {Z}_+$, where $\alpha$ is given by a cocycle $c$. We show that the maximal ideal space $\mathcal {M}$ of $C^*(G,\sigma )\times _\alpha \mathbb {Z}_+$ depends on the asymptotic range of $c$, $R_\infty (c)$; that is, $\mathcal {M}$ is homeomorphic to $\overline { \mathbb {D}}\mid R_\infty (c)$ for $R_\infty (c)$ finite, and $\mathcal {M}$ consists of the unique maximal ideal for $R_\infty (c)= \mathbb {T}$. We also prove that $C^*(G,\sigma )\times _\alpha \mathbb {Z}_+$ is semisimple in both cases, and that $R_\infty (c)$ is invariant under isometric isomorphism.References
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Additional Information
- Miron Shpigel
- Affiliation: Department of Mathematics, Technion — Israel Institute of Technology, 3200 Haifa, Israel
- Email: meshpigel@math.uwaterloo.ca
- Received by editor(s): December 2, 1996
- Published electronically: February 15, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 2515-2538
- MSC (1991): Primary 47D25; Secondary 46H10, 46L05
- DOI: https://doi.org/10.1090/S0002-9947-99-02221-7
- MathSciNet review: 1475694