✦ LIBER ✦
Semisimple Banach Algebras Generated by Strongly Continuous Representations of Locally Compact Abelian Groups
✍ Scribed by G. Muraz; V.Q. Phong
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 207 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
We prove that if (T) is a strongly based continuous bounded representation of a locally compact abelian group (G) on a Banach Space (X), and if the spectrum of (T) is countable, then the Banach algebra generated by (f(T)=\int_{G} f(g) T(g) d g), (f \in L^{1}(G)), is semisimple. 1994 Academic Press, Inc.