Amenability for Fell bundles over groupoids

@article{Sims2012AmenabilityFF,
  title={Amenability for Fell bundles over groupoids},
  author={Aidan Sims and Dana P. Williams},
  journal={Illinois Journal of Mathematics},
  year={2012},
  volume={57},
  pages={429-444}
}
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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References

SHOWING 1-10 OF 22 REFERENCES

An equivalence theorem for reduced Fell bundle C*-algebras

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional

Equivalence and disintegration theorems for Fell bundles and their C*-algebras

We study the C*-algebras of Fell bundles. In particular, we prove the analogue of Renault's disintegration theorem for groupoids. As in the groupoid case, this result is the key step in proving a

RENAULT'S EQUIVALENCE THEOREM FOR GROUPOID CROSSED PRODUCTS

We provide an exposition and proof of Renault's equivalence theo- rem for crossed products by locally Hausdorff, locally compact groupoids. Our approach stresses the bundle approach, concrete

On a duality for crossed products of C∗-algebras

Morita Equivalence and Continuous-Trace $C^*$-Algebras

The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actions

Higher Rank Graph C-Algebras

Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of

A Classic Morita Equivalence Result for Fell Bundle C*-algebras

We show how to extend a classic Morita Equivalence Result of Green's to the \cs-algebras of Fell bundles over transitive groupoids. Specifically, we show that if $p:\B\to G$ is a saturated Fell

Haar measure for measure groupoids

It is proved that Mackey's measure groupoids possess an analogue of Haar measure for locally compact groups; and many properties of the group Haar measure generalize. Existence of Haar measure for

Remarks on the Ideal Structure of Fell Bundle C*-Algebras

We show that if $p:\B\to G$ is a Fell bundle over a locally compact groupoid $G$ and that $A=\Gamma_{0}(G^{(0)};\B)$ is the \cs-algebra sitting over $G^{(0)}$, then there is a continuous $G$-action

On higher rank graph C ∗ -algebras

Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C *-algebra, C * (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C