arXiv 1809.040972018-09-11math.FA

Norm-controlled inversion in weighted convolution algebras

Ebrahim Samei, Varvara Shepelska

英文摘要：

Let $G$ be a discrete group, let $p\ge1$, and let $ω$ be a weight on $G$. Using the approach from [9], we provide sufficient conditions on a weight $ω$ for $\ell^p(G,ω)$ to be a Banach algebra admitting a norm-controlled inversion in the reduced C$^*$-algebra of $G$, namely $C^*_r(G)$. We show that our results can be applied to various cases including locally finite groups as well as finitely generated groups of polynomial or intermediate growth and a natural class of weights on them. These weights are of the form of polynomial or certain subexponential functions. We also consider the non-discrete case and study the existence of norm-controlled inversion in $B(L^2(G))$ for some related convolution algebras.

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