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The decomposition of representations induced by arithmetic subgroups of semisimple algebraic groups

โœ Scribed by R. G. Laha


Publisher
Springer US
Year
1969
Tongue
English
Weight
221 KB
Volume
3
Category
Article
ISSN
0016-2663

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Semisimple Banach Algebras Generated by
โœ G. Muraz; V.Q. Phong ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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