2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79448A separable Banach space X contains $\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system.Functional Analysis46B20 (primary) 46B25, 46B99 (secondary)text