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This analysis explores spectral invariance in Roe algebras for discrete groups with subexponential growth, suggesting new pathways for understanding algebraic structures.
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.
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Jiang et al. (2025) studied this question.
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