Perfect measures and the dunford-pettis property

• Aguayo G., José ^[1] ; Sánchez H., José ^[1]
  1. [1] Universidad de Concepción

     Universidad de Concepción

     Comuna de Concepción, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 11, Nº. 2, 1992, págs. 125-129
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Let X be a completely regular Hausdorff space. We denote by Cb(X) the Banach space of all real-valued bounded continuous function's on X endowed with the supremum-norm. Mp(X) denotes the subspace of the (Cb(X), II II)' of all perfect measures on X and βp denotes a topology on Cb(X) whose dual is Mp(X).In this paper we give a characterization of E-valued weakly compact operators which are β-continuous on Cb(X), where E denotes a Banach space. We also prove that (Cb(X),( βp) has strict Dunford-Pettis property and, if X contains a σ-compact dense subset, (Cb(X), βp) has Dunford-Pettis property.