Biduality and density in Lipschitz function spaces

• A. Jiménez-Vargas ^[1] ; J. M. Sepulcre ^[3] ; M. Villegas-Vallecillos ^[2]
  1. [1] Universidad de Almería

     Universidad de Almería

     Almería, España

     
  2. [2] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
  3. [3] Universitat d'Alacant

     Universitat d'Alacant

     Alicante, España

     

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• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 121, Nº 1, 2017, págs. 92-100
• Idioma: inglés
• DOI: 10.7146/math.scand.a-25987
• Texto completo no disponible (Saber más ...)
• Resumen

  • For pointed compact metric spaces (X,d), we address the biduality problem as to when the space of Lipschitz functions Lip0(X,d) is isometrically isomorphic to the bidual of the space of little Lipschitz functions lip0(X,d), and show that this is the case whenever the closed unit ball of lip0(X,d) is dense in the closed unit ball of Lip0(X,d) with respect to the topology of pointwise convergence. Then we apply our density criterion to prove in an alternative way the real version of a classical result which asserts that Lip0(X,dα) is isometrically isomorphic to lip0(X,dα)∗∗ for any α∈(0,1).