Spectral continuity for \'etale groupoids with the Rapid decay property
Operator Algebras
2025-09-30 v1
Abstract
We show that the reduced groupoid C*-algebras of continuous fields of \'etale groupoids satisfying the rapid decay property yield continuous fields of C*-algebras. This establishes a new sufficient criterion that applies in the non-amenable case where the full and reduced groupoid algebras may differ. Potential applications include convergence of spectra in inverse systems of finite-index subgroups and magnetic models on hyperbolic lattices.
Keywords
Cite
@article{arxiv.2509.24145,
title = {Spectral continuity for \'etale groupoids with the Rapid decay property},
author = {Tom Stoiber},
journal= {arXiv preprint arXiv:2509.24145},
year = {2025}
}