Biduality and density in Lipschitz function spaces

  1. A. Jiménez-Vargas 1
  2. J. M. Sepulcre 3
  3. M. Villegas-Vallecillos 2
  1. 1 Universidad de Almería
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    Universidad de Almería

    Almería, España

    ROR https://ror.org/003d3xx08

    Geographic location of the organization Universidad de Almería
  2. 2 Universidad de Cádiz
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    Universidad de Cádiz

    Cádiz, España

    ROR https://ror.org/04mxxkb11

    Geographic location of the organization Universidad de Cádiz
  3. 3 Universitat d'Alacant
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    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

    Geographic location of the organization Universitat d'Alacant
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Journal:
Mathematica scandinavica

ISSN: 0025-5521

Year of publication: 2017

Volume: 121

Issue: 1

Pages: 92-100

Type: Article

DOI: 10.7146/MATH.SCAND.A-25987 DIALNET GOOGLE SCHOLAR

More publications in: Mathematica scandinavica

Abstract

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).

Data source: Dialnet