Equivalence of Fell bundles over groups

Abstract

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable. The equivalence between two Fell bundles is implemented by a bundle of Hilbert bimodules with some extra structure. Suitable cross-sectional spaces of such a bundle turn out to be imprimitivity bimodules for the cross-sectional C∗-algebras of the involved Fell bundles. We show that amenability is preserved under this equivalence.