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 http://arXiv.org/abs/1510.01531