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 $T_{0}$, 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.
Citation
Aidan Sims. Dana P. Williams. "Amenability for Fell bundles over groupoids." Illinois J. Math. 57 (2) 429 - 444, Summer 2013. https://doi.org/10.1215/ijm/1408453589
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