English

Dual maps and the Dunford-Pettis property

Functional Analysis 2015-10-07 v1

Abstract

We characterize the points of \left\|\cdot\right\|-ww^* 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 ww-ww continuous at 00. As consequence, we show the existence of smooth Banach spaces on which the dual map is not ww-ww continuous at 00.

Keywords

Cite

@article{arxiv.1510.01531,
  title  = {Dual maps and the Dunford-Pettis property},
  author = {Francisco J. García-Pacheco and Alejandro Miralles and Daniele Puglisi},
  journal= {arXiv preprint arXiv:1510.01531},
  year   = {2015}
}

Comments

6 pages