On operator Connes-amenability of the Fourier-Stieltjes algebra
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| Format: | Preprint |
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2025
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| _version_ | 1866909017915260928 |
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| author | Runde, Volker Spronk, Nico Wiersma, Matthew |
| author_facet | Runde, Volker Spronk, Nico Wiersma, Matthew |
| contents | Runde and Spronk showed in 2004 that there are non-amenable groups $G$, including $\mathbb F_2$, {whose Fourier-Stieltjes algebra, $B(G)$,} is operator Connes-amenable. This result was surprising since the measure algebra $M(G)$ is Connes-amenable if and only if $G$ is amenable, which might lead one to guess that $B(G)$ should be operator Connes-amenable if and only if $G$ is amenable. This leads to the question: for which groups $G$ is $B(G)$ operator Connes-amenable? We make progress on this problem by {exhibiting} the first examples of groups {for which $B(G)$ is not operator Connes-amenable}. More specifically, we show that $B(G)$ is not operator Connes-amenable when $G$ is a non-compact locally compact group with property (T) and finite almost periodic compactification, or when $G$ is a discrete group without the factorization property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On operator Connes-amenability of the Fourier-Stieltjes algebra Runde, Volker Spronk, Nico Wiersma, Matthew Functional Analysis Group Theory Operator Algebras Runde and Spronk showed in 2004 that there are non-amenable groups $G$, including $\mathbb F_2$, {whose Fourier-Stieltjes algebra, $B(G)$,} is operator Connes-amenable. This result was surprising since the measure algebra $M(G)$ is Connes-amenable if and only if $G$ is amenable, which might lead one to guess that $B(G)$ should be operator Connes-amenable if and only if $G$ is amenable. This leads to the question: for which groups $G$ is $B(G)$ operator Connes-amenable? We make progress on this problem by {exhibiting} the first examples of groups {for which $B(G)$ is not operator Connes-amenable}. More specifically, we show that $B(G)$ is not operator Connes-amenable when $G$ is a non-compact locally compact group with property (T) and finite almost periodic compactification, or when $G$ is a discrete group without the factorization property. |
| title | On operator Connes-amenability of the Fourier-Stieltjes algebra |
| topic | Functional Analysis Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2512.13464 |