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The Quarterly Journal of Mathematics Advance Access published online on December 11, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham034
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© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

SEMISIMPLE BANACH ALGEBRAS GENERATED BY STRONGLY CONTINUOUS REPRESENTATIONS OF MOORE GROUPS

J. Alaminos{dagger}, J. Extremera {ddagger} and A. R. Villena §

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

{dagger} Corresponding author. E-mail: alaminos{at}ugr.es

Received 14 November 2006;
  Abstract

We prove that if {tau} is a strongly continuous bounded representation of a Moore group G on a Banach space X, and if the Arveson spectrum of {tau} is scattered, then the closure with respect to the weak operator topology in L(X) of the algebra generated by the transformsisintGf(t){tau}(t)d t with fisinL1(G) is a semisimple Banach algebra.

{ddagger} E-mail: jlizana{at}ugr.es

§ E-mail: avillena{at}ugr.es


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