2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95176Let $G$ be a locally compact group, and let $WAP(G)$ denote the space of weakly almost periodic functions on $G$. We show that, if $G$ is a $[SIN]$-group, but not compact, then the dual Banach algebra $WAP(G)^\ast$ does not have a normal, virtual diagonal. Consequently, whenever $G$ is an amenable, non-compact $[SIN]$-group, $WAP(G)^\ast$ is an example of a Connes-amenable, dual Banach algebra without a normal,virtual diagonal.16 pages; some more, minor revisionsFunctional AnalysisOperator Algebras22A15, 22A20, 43A07, 43A10, 43A60, 46H20 (primary) 46H25, 46M18, 46M20text