2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75137We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson (1977) : "If a normed space $E$ does not contain any asymptotically isometric copy of $\ell^1(\IN)$, then every bounded sequence of $E'$ has a normalized block sequence pointwise converging to 0".Functional Analysis46B ; 03E25text