Abstract
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 ∫ G f(t) τ (t)d t with f ∈ L 1 (G) is a semisimple Banach algebra.
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