Journal Article

SEMISIMPLE BANACH ALGEBRAS GENERATED BY STRONGLY CONTINUOUS REPRESENTATIONS OF MOORE GROUPS

J. Alaminos, J. Extremera and A. R. Villena

in The Quarterly Journal of Mathematics

Volume 59, issue 2, pages 137-147
Published in print June 2008 | ISSN: 0033-5606
Published online December 2007 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/ham034
SEMISIMPLE BANACH ALGEBRAS GENERATED BY STRONGLY CONTINUOUS REPRESENTATIONS OF MOORE GROUPS

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We prove that if τ is a strongly continuous bounded representation of a Moore group G on a Banach space X, and if the Arveson spectrum of τ is scattered, then the closure with respect to the weak operator topology in L(X) of the algebra generated by the transforms ∫ Gf(t) τ (t)d t with fL1(G) is a semisimple Banach algebra.

Journal Article.  0 words. 

Subjects: Pure Mathematics

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