2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130811We give an example of a non-compact, locally compact group $G$ such that its Fourier-Stieltjes algebra $B(G)$ is operator amenable. Furthermore, we characterize those $G$ for which $A^*(G)$ - the spine of $B(G)$ as introduced by M. Ilie and the second named author - is operator amenable and show that $A^*(G)$ is operator weakly amenable for each $G$.12 pages; AMSLaTeX; references updated & some typos caughtFunctional AnalysisOperator AlgebrasPrimary 43A30; Secondary 22D10, 22D25, 43A65, 46L07, 47L25, 47L50text