Almost Weakly Compact Operators

Volume 54 / 2006

Ioana Ghenciu, Paul Lewis Bulletin Polish Acad. Sci. Math. 54 (2006), 237-256 MSC: 46B20, 46B25, 46B28. DOI: 10.4064/ba54-3-6


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.


  • Ioana GhenciuDepartment of Mathematics
    University of Wisconsin at River Falls
    River Falls, WI 54022, U.S.A.
  • Paul LewisDepartment of Mathematics
    University of North Texas
    Box 311430
    Denton, TX 76203-1430, U.S.A.

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