Locally compact group actions on C∗-algebras and compact subgroups
✍ Scribed by Costel Peligrad
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 690 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0022-1236
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📜 SIMILAR VOLUMES
## Abstract In the present paper we introduce a new definition for the Fourier space __A__ (__K__) of a locally compact Hausdorff hypergroup __K__ and prove that it is a Banach subspace of __B__ (__K__). This definition coincides with that of Amini and Medghalchi in the case where __K__ is a tensor
Let \(G\) be a locally compact group and \(\mathrm{VN}(G)\) be the von Neumann algebra generated by the left regular representation of \(G\). Let \(\operatorname{UCB}(\hat{G})\) denote the \(C^{*}\)-subalgebra generated by operators in \(\mathrm{VN}(G)\) with compact support. When \(G\) is abelian.
Let \(\alpha\) be an action of a compact group on a separable prime \(C^{*}\)-algebra \(A\). Several conditions on \(\alpha\) are shown to be equivalent, among which are the following two: there exists a faithful irreducible representation of \(A\) which is also irreducible on \(A^{x}\); there exi