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Convex smooth-like properties and Faces Radon–Nikodým property in Banach spaces

Volume 240 / 2018

David Salas Studia Mathematica 240 (2018), 213-253 MSC: Primary 46B20; Secondary 46B22, 46G05. DOI: 10.4064/sm8440-3-2017 Published online: 18 September 2017

Abstract

We introduce the notion of convex smooth-like (resp. $w^*$-smooth-like) properties, which are a generalization of the well-known Asplund (resp. $w^*$-Asplund) property. We show that many of the reductions made for the Asplund property also work for these smooth-like properties. In this framework, we introduce a new geometrical property, called the Faces Radon–Nikodým property, and we prove that it is in duality with a convex $w^*$-smooth-like property.

Authors

  • David SalasInstitut Montpelliérain Alexander Grothendieck
    Université de Montpellier
    34095 Montpellier Cedex 05, France
    and
    CNRS PROMES – UPR 8521
    Tecnosud
    F-66100 Perpignan, France
    e-mail

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