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October 8, 2025Open Access

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

Key Points

Spectral invariance holds for subalgebras in Roe algebras of groups with subexponential growth, extending existing results.
A class of subalgebras, denoted as R^{B8}(G), is constructed specifically for groups satisfying property P and showing subexponential growth.
Using admissible weights, the proof for the spectral invariance in C_u^*(G) is established, offering broader implications.
This work enhances understanding of algebraic structures in discrete groups, highlighting differences from polynomial growth settings.

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^ (G). We then prove their spectral invariance in Cᵤ^* (G) through the application of admissible weights. This extends ²-norm spectral invariance results beyond polynomial growth settings.

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

Key Points

Abstract

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