Ghenciu, Ioana; Lewis, Paul Almost weakly compact operators. (English) Zbl 1118.46016 Bull. Pol. Acad. Sci., Math. 54, No. 3-4, 237-256 (2006). 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. Cited in 9 Documents 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 Keywords:Dunford-Pettis property; Dunford-Pettis sets; limited sets; \(L\)-sets; \(w^*\)-\(w\) continuity; almost weakly compact operator PDFBibTeX XMLCite \textit{I. Ghenciu} and \textit{P. Lewis}, Bull. Pol. Acad. Sci., Math. 54, No. 3--4, 237--256 (2006; Zbl 1118.46016) Full Text: DOI