Morita enveloping Fell bundles

Abstract

We introduce notions of weak and strong equivalence for non-saturated Fell bundles over locally compact groups and show that every Fell bundle is strongly (resp. weakly) equivalent to a semidirect product Fell bundle for a partial (resp. global) action. Equivalences preserve cross-sectional $C^{\ast }-$algebras and amenability. We use this to show that previous results on crossed products and amenability of group actions carry over to Fell bundles.

This version contains some comments and references to a recent work by Kwaśniewski and Meyer

Cited by in corpus (3)

• Stone duality and quasi-orbit spaces for generalised C*-inclusions
• Amenability and approximation properties for partial actions and Fell bundles
• Positive definiteness and Fell bundles over discrete groups