2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69487We give biorthogonal system characterizations of Banach spaces that fail the Dunford-Pettis property, contain an isomorphic copy of $c_0$, or fail the hereditary Dunford-Pettis property. We combine this with previous results to show that each infinite dimensional Banach space has one of three types of biorthogonal systems.22 pagesFunctional Analysis46B20; 46B25text