Exactness and Fell bundles with the approximation property over inverse semigroups
Abstract
We prove that the reduced cross-sectional algebra of a Fell bundle with the approximation property over an inverse semigroup is exact if and only if the unit fiber of the Fell bundle is exact. This generalizes a recent result of the first-named author for actions of second countable locally compact Hausdorff groupoids on separable $C^*$-algebras. Along the way, we reprove some results of Kwaśniewski--Meyer on Fell bundle ideals.
Fields of Study & Subjects
Advanced Operator Algebra Research
Holomorphic and Operator Theory
Advanced Banach Space Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 January 2026
- Document type
- Preprint