2010/03/08 by Christian Le Merdy, Merdy, Christian Le
Mathematics · #22D12 #46B28 #47A60 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:22D12 #msc:46B28 #msc:47A60
paper · pdf · doi:10.48550/arxiv.1003.1587
arxiv created 2010/03/08 · openalex publication_date 2010/03/08 · arxiv updated 2010/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let G be an amenable group, let X be a Banach space and let π: G --> B(X) be a bounded representation. We show that if the set π(t) : t ∈ G is gamma-bounded then πextends to a bounded homomorphism w : C*(G) --> B(X) on the group C*-algebra of G. Moreover w is necessarily gamma-bounded. This extends to the Banach space setting a theorem of Day and Dixmier saying that any bounded representation of an amenable group on Hilbert space is unitarizable. We obtain additional results and complements when G is equal to either the real numbers, the integers or the unit circle, and/or when X has property (α).