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Positivity

, Volume 13, Issue 1, pp 129–143 | Cite as

Ordered representations of spaces of integrable functions

  • Antonio Fernández
  • Fernando Mayoral
  • Francisco Naranjo
  • Enrique A. Sánchez–Pérez
Article
  • 36 Downloads

Abstract

Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L1(n) = L1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L1(m) associated to downward directed subsets of the set of all the representations.

Keywords

Banach function space Vector measure Representation 

Mathematics Subject Classififcation (2000)

Primary 46E30, 46G10 Secondary 47B65, 47H07 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Antonio Fernández
    • 1
  • Fernando Mayoral
    • 1
  • Francisco Naranjo
    • 1
  • Enrique A. Sánchez–Pérez
    • 2
  1. 1.Dpto. Matemática Aplicada IIEscuela Técnica Superior de IngenierosSevillaSpain
  2. 2.Instituto Universitario de Matemática Pura y Aplicada (I.U.M.P.A.)Universidad Politécnica de ValenciaValenciaSpain

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