2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158721Let $C$ be a closed convex cone in a Banach ideal space $X$ on a measurable space with a $σ$-finite measure. We prove that conditions $C\cap X_+=\{0\}$ and $C\supset -X_+$ imply the existence of a strictly positive continuous functional on $X$, whose restriction to $C$ is non-positive.6 pagesFunctional Analysis46E30; 46B42text