2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60115We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of $l_1$. We show that a normalized unconditional basic sequence in $l_1$ that is semi-normalized in $l_\infty$ is equivalent to the standard unit vector basis of~$l_1$.Latex. 8 pgsFunctional Analysis46B45 (Primary), 46B15 (Secondary)text