2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70097We study a semigroup $ϕ$ of linear operators acting on a Banach space $X$ which satisfies the condition $\codim X_0<\infty$, where $X_0=\{x\in X \mid ϕ_t(x)\underset{t\to\infty}\longrightarrow 0\}.$ We show that $X_0$ is closed under these conditions. We establish some properties concerning the asymptotic behavior of subspaces which complement $X_0$ in $X$.10 pagesFunctional Analysis47D03text