Almost Weakly Compact Operators
Dunford–Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford–Pettis property. The question of whether a space of operators has a Dunford–Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.