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

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae 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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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.