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Approximation of integration maps of vector measures and limit representations of Banach function spaces

Volume 120 / 2017

Eduardo Jiménez Fernández, Enrique A. Sánchez Pérez, Dirk Werner Annales Polonici Mathematici 120 (2017), 63-81 MSC: Primary 46G10, 28B05; Secondary 46E30, 47B07, 47B38. DOI: 10.4064/ap170407-21-9 Published online: 8 November 2017


We study whether or not the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon–Nikodým derivatives. The positive cases are obtained by using the circle of ideas related to the approximation property for Banach spaces. The negative ones are given by means of an appropriate use of the Daugavet property. As an application, we analyse when the norm in a space $L^1(m)$ of integrable functions can be computed as a limit of the norms of the spaces of integrable functions with respect to the Radon–Nikodým derivatives of $m$.


  • Eduardo Jiménez FernándezDepartamento de Economía
    Universitat Jaume I
    Campus del Riu Sec, s/n
    12071 Castelló de la Plana, Spain
  • Enrique A. Sánchez PérezInstituto Universitario de Matemática Pura y Aplicada
    Universitat Politècnica de València
    Camino de Vera, s/n
    46022 València, Spain
  • Dirk WernerFachbereich Mathematik und Informatik
    Freie Universität Berlin
    Arnimallee 6
    14195 Berlin, Germany

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