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SEMISIMPLE BANACH ALGEBRAS GENERATED BY STRONGLY CONTINUOUS REPRESENTATIONS OF MOORE GROUPS

Authors:	Alaminos, J. Extremera, J. Villena, A. R.

Affiliation:	Departamento de Análisis Matemático. Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract:	We prove that if ${tau}$ is a strongly continuous bounded representationof a Moore group G on a Banach space X, and if the Arveson spectrumof ${tau}$ is scattered, then the closure with respect to the weakoperator topology in L(X) of the algebra generated by the transforms ${int}$ _Gf(t) ${tau}$ (t)d t with f $isin$ L¹(G) is a semisimple Banach algebra.

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