This is an announcement for the paper "Dual maps and the Dunford-Pettis property" by Francisco J. Garcia-Pacheco, Alejandro Miralles, and Daniele Puglisi.
Abstract: We characterize the points of $\left|\cdot\right|$-$w^*$ 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 $0$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B10
Remarks: 6 pages
Submitted from: mirallea@uji.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.01531
or