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Almost weakly compact operators. (English) Zbl 1118.46016

Summary: 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.

MSC:

46B03 Isomorphic theory (including renorming) of Banach spaces
46B25 Classical Banach spaces in the general theory
46B28 Spaces of operators; tensor products; approximation properties
47B07 Linear operators defined by compactness properties
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