Spectral continuity for étale groupoids with the Rapid decay property
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916975066742784 |
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| author | Stoiber, Tom |
| author_facet | Stoiber, Tom |
| contents | We show that the reduced groupoid C*-algebras of continuous fields of étale 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral continuity for étale groupoids with the Rapid decay property Stoiber, Tom Operator Algebras We show that the reduced groupoid C*-algebras of continuous fields of étale 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. |
| title | Spectral continuity for étale groupoids with the Rapid decay property |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2509.24145 |