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

2025/07/23 by Jiang, Siqi, Xianjin Wang, Wang, Xianjin
Mathematics · #346L05 #46L80 #47L40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2507.17322

openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C_u^*(G) through the application of admissible weights. This extends ℓ²-norm spectral invariance results beyond polynomial growth settings.

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