2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73365A Banach space $X$ is said to have the alternative Daugavet property if for every (bounded and linear) rank-one operator $T:X\longrightarrow X$ there exists a modulus one scalar $ω$ such that $\|Id + ωT\|= 1 + \|T\|$. We give geometric characterizations of this property in the setting of $C^*$-algebras, $JB^*$-triples and their isometric preduals.Functional AnalysisOperator Algebras46B20, 46L05, 17C65 (primary); 47A12 (secondary)text