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

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 $C_u^{\ast }(G)$ through the application of admissible weights. This extends ${\ell }^2$-norm spectral invariance results beyond polynomial growth settings.