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arXiv · 2403.06945

A note on ideal C$^\ast$-completions and amenability

Tomasz Kochanek
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Abstract

For a discrete group $G$, we consider certain ideals $\mathcal{I}\subset c_0(G)$ of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$^\ast$-algebra of $G$ and the C$^\ast$-completion $\mathrm{C}_{\mathcal{I}}^\ast(G)$ in the sense of Brown and Guentner implies that $G$ is amenable.

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Tomasz Kochanek. 2024-03-11. A note on ideal C$^\ast$-completions and amenability. https://arxiv.org/abs/2403.06945

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