Biduality and density in Lipschitz function spaces

  1. Antonio Jiménez Vargas 1
  2. Juan Matías Sepulcre Martínez 3
  3. Moisés Villegas-Vallecillos 2
  1. 1 Universidad de Almería (España)
  2. 2 Universidad de Cádiz (España)
  3. 3 Universidad de Alicante (España)
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Revue:
Mathematica scandinavica

ISSN: 0025-5521

Année de publication: 2017

Volumen: 121

Número: 1

Pages: 92-100

Type: Article

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

D'autres publications dans: Mathematica scandinavica

Résumé

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).

La source de données: Dialnet