Amenability for Fell bundles over groupoids

2012/01/04 by Aidan Sims, Sims, Aidan, Dana P. Williams +1
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.1201.0792

13 pages

arxiv created 2012/01/04 · openalex publication_date 2012/01/04 · arxiv updated 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish conditions under which the universal and reduced norms coincide for a Fell bundle over a groupoid. Specifically, we prove that the full and reduced C*-algebras of any Fell bundle over a measurewise amenable groupoid coincide, and also that for a groupoid G whose orbit space is T₀, the full and reduced algebras of a Fell bundle over G coincide if the full and reduced algebras of the restriction of the bundle to each isotropy group coincide.

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