An explicit minorant for the amenability constant of the Fourier algebra

Choi, Yemon (2023) An explicit minorant for the amenability constant of the Fourier algebra. International Mathematics Research Notices, 2023 (22). 19390–19430. ISSN 1073-7928

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We show that if a locally compact group $G$ is non-abelian, then the amenability constant of its Fourier algebra is $\geq 3/2$, extending a result of [9] who proved that this holds for finite non-abelian groups. Our lower bound, which is known to be best possible, improves on results by previous authors and answers a question raised by [16]. To do this, we study a minorant for the amenability constant, related to the anti-diagonal in $G\times G$, which was implicitly used in Runde’s work but hitherto not studied in depth. Our main novelty is an explicit formula for this minorant when $G$ is a countable virtually abelian group, in terms of the Plancherel measure for $G$. As further applications, we characterize those non-abelian groups where the minorant attains its minimal value and present some examples to support the conjecture that the minorant always coincides with the amenability constant.

Item Type:
Journal Article
Journal or Publication Title:
International Mathematics Research Notices
Uncontrolled Keywords:
?? amenability constantfourier algebragroup theorymathematics(all) ??
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Deposited On:
06 Dec 2022 14:45
Last Modified:
29 Feb 2024 01:18