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 Acad
Banach uniformly continuous representations of Lie groups and algebras
โ Scribed by David Gurarie
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 393 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0022-1236
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