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

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 $R^{\mathrm{\infty }}(G)$. We then prove their spectral invariance in $C_u^{\ast }(G)$ through the application of admissible weights. This extends ${\mathrm{\ell }}^2$-norm spectral invariance results beyond polynomial growth settings.