A note on ideal C $$^*$$ -completions and amenability

Pub Date : 2024-05-10 DOI:10.1007/s00010-024-01077-x

Tomasz Kochanek

引用次数: 0

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$^*$-algebra of G and the C$^*$-completion $\textrm{C}^*_{\mathcal {I}}(G)$ in the sense of Brown and Guentner (Bull. London Math. Soc. 45:1181–1193, 2013) implies that G is amenable.

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关于理想 C $$^*$$ -补全和可亲和性的说明

对于离散群 G，我们考虑了某些序列的理想（(\mathcal {I}\subset c_0(G)\) of sequences with prescribed rate of convergence to zero）。我们证明，在布朗和根特纳（Bull. London Math. Soc. 45:1181-1193，2013）的意义上，G 的全群 C$^*$-algebra 与 C$^*$-completion $\textrm{C}^*_{mathcal {I}}(G)$之间的相等性意味着 G 是可封闭的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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