## Illinois Journal of Mathematics

### Amenability for Fell bundles over groupoids

#### 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.

#### Article information

Source
Illinois J. Math., Volume 57, Number 2 (2013), 429-444.

Dates
First available in Project Euclid: 19 August 2014

https://projecteuclid.org/euclid.ijm/1408453589

Digital Object Identifier
doi:10.1215/ijm/1408453589

Mathematical Reviews number (MathSciNet)
MR3263040

Zentralblatt MATH identifier
1297.46047

#### Citation

Sims, Aidan; Williams, Dana P. Amenability for Fell bundles over groupoids. Illinois J. Math. 57 (2013), no. 2, 429--444. doi:10.1215/ijm/1408453589. https://projecteuclid.org/euclid.ijm/1408453589

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