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This analysis reveals a sufficient criterion linking rapid decay in étale groupoids to C-algebras, indicating potential applications in spectral convergence and magnetic models.
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.
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Tom Stoiber (2025) studied this question.
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