Duality, reflexivity and atomic decompositions in Banach spaces

Volume 191 / 2009

Daniel Carando, Silvia Lassalle Studia Mathematica 191 (2009), 67-80 MSC: Primary 41A65, 46B10; Secondary 42C15, 46B15. DOI: 10.4064/sm191-1-5

Abstract

We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of “shrinking” and “boundedly complete” Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions.

Authors

  • Daniel CarandoDepartamento de Matemática - Pab I
    Facultad de Cs. Exactas y Naturales
    Universidad de Buenos Aires
    (1428) Buenos Aires, Argentina
    and
    CONICET
    e-mail
  • Silvia LassalleDepartamento de Matemática - Pab I
    Facultad de Cs. Exactas y Naturales
    Universidad de Buenos Aires
    (1428) Buenos Aires, Argentina
    and
    CONICET
    e-mail

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