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Semisimple Banach algebras generated by compact groups of operators on a Banach space

✍ Scribed by José E. Galé; Armando R. Villena

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
110 KB
Volume
325
Category
Article
ISSN
0022-247X

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Semisimple Banach Algebras Generated by
Semisimple Banach Algebras Generated by Strongly Continuous Representations of Locally Compact Abelian Groups
✍ G. Muraz; V.Q. Phong 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 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