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arXiv · 2507.17322

On Spectral Invariant Dense Subalgebras of Uniform Roe Algebras with Subexponential Growth

Siqi Jiang·Xianjin Wang
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Abstract

In this paper, we study spectrally invariant subalgebras of uniform Roe algebras for discrete groups with subexponential growth. For a group $G$ with subexponential growth and satisfying property $P$, we construct a class of subalgebras $R^{\infty}(G)$. We then prove their spectral invariance in $C_u^*(G)$ through the application of admissible weights. This extends $\ell^2$-norm spectral invariance results beyond polynomial growth settings.

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Siqi Jiang, Xianjin Wang. 2025-07-23. On Spectral Invariant Dense Subalgebras of Uniform Roe Algebras with Subexponential Growth. https://arxiv.org/abs/2507.17322

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