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Commutative Banach algebras generated by a group of unitary elements

✍ Scribed by E. A. Gorin

Publisher
Springer US
Year
1968
Tongue
English
Weight
136 KB
Volume
1
Category
Article
ISSN
0016-2663

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πŸ“œ SIMILAR VOLUMES

Semisimple Banach Algebras Generated by
Semisimple Banach Algebras Generated by Strongly Continuous Representations of Locally Compact Abelian Groups
✍ G. Muraz; V.Q. Phong πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 207 KB

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