On the weak Dunford-Pettis property (Q1100682)

A Banach space E has the Dunford-Pettis property if every weakly compact operator from E into any Banach space is a Dunford-Pettis operator, i.e., maps weakly compact sets onto norm compact sets. A Banach lattice E has the weak Dunford-Pettis property if every weakly compact operator from E into any Banach space maps disjoint, weakly null sequences onto norm null sequences. We provide an example which serves to distinguish these two properties.