Weak-star point of continuity property and Schauder bases

Tom 219 / 2013

Ginés López-Pérez, José A. Soler-Arias Studia Mathematica 219 (2013), 225-236 MSC: Primary 46B20; Secondary 46B22. DOI: 10.4064/sm219-3-3

Streszczenie

We characterize the weak-star point of continuity property for subspaces of dual spaces with separable predual and we deduce that the weak-star point of continuity property is determined by subspaces with a Schauder basis in the natural setting of dual spaces of separable Banach spaces. As a consequence of the above characterization we show that a dual space has the Radon–Nikodym property if, and only if, every seminormalized topologically weak-star null tree has a boundedly complete branch, which improves some results of Dutta and Fonf (2008) obtained for the separable case. Also, as a consequence of the above characterization, the following result of Rosenthal (2007) is deduced: every seminormalized basic sequence in a Banach space with the point of continuity property has a boundedly complete subsequence.

Autorzy

  • Ginés López-PérezUniversidad de Granada
    Facultad de Ciencias
    Departamento de Análisis Matemático
    18071 Granada, Spain
    e-mail
  • José A. Soler-AriasUniversidad de Granada
    Facultad de Ciencias
    Departamento de Análisis Matemático
    18071 Granada, Spain
    e-mail

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