2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97325For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than or equal to $\sup \{°(π) : π\in \hat{G} \}$ and that it is equal to one if and only if $G$ is abelian.LaTeX2e; 11 pages; some more minor revisionsFunctional AnalysisPrimary 46H20; Secondary 20B99, 22D05, 22D10, 43A40, 46J10, 46J40, 46L07, 47L25, 47L50text