2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79340The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of c, the Banach space of null sequences under the supremum norm, or there exists a subsequence which is boundedly convexly complete. This result generalizes J. Elton's dichotomy on weakly null sequences.44 pages, AMS-LaTexFunctional Analysis46B03text