2015/10/06 by Francisco Javier García‐Pacheco, García-Pacheco, Francisco J., Alejandro Miralles +3
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.1510.01531
We characterize the points of ‖⋅‖-w^* continuity of dual maps, turning out to be the smooth points. We prove that a Banach space has the Schur property if and only if it has the Dunford-Pettis property and there exists a dual map that is sequentially w-w continuous at 0. As consequence, we show the existence of smooth Banach spaces on which the dual map is not w-w continuous at 0.