Exactness and Fell bundles with the approximation property over inverse semigroups
Operator Algebras
2026-05-21 v2
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 -algebras. Along the way, we reprove some results of Kwa\'sniewski--Meyer on Fell bundle ideals.
Keywords
Cite
@article{arxiv.2601.07572,
title = {Exactness and Fell bundles with the approximation property over inverse semigroups},
author = {Changyuan Gao and Julian Kranz},
journal= {arXiv preprint arXiv:2601.07572},
year = {2026}
}
Comments
18 pages. Minor changes. Adjusted the title to avoid terminological conflicts with Kwa\'sniewski--Meyer's definition of exact Fell bundles