The C*-Algebra Generated by Operators with Compact Support on a Locally Compact Group
✍ Scribed by A.T.M. Lau; V. Losert
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 997 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
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. LCB ((\hat{G})) corresponds to the space of bounded uniformly continuous functions on the dual group (\hat{G}) of (G). In this paper we prove among other things that for a large class of locally compact groups which include the Heisenterg group, the (" a x+b ") group and the motion group, the centre of the Banach algebra UCB ((\dot{G})^{}) is the Fourier Stieljes algebra (B(G)). ' 1993 Aedemic Press. Inc