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
• DOI: 10.22199/S07160917.1992.0002.00004
• 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.

• Referencias bibliográficas
  • Citas [1] Aguayo, J.; Sánchez, J.: Weakly Compact Operators and the Strict Topologies. Bull. Austral. Math. Soc., 39, 1989.
  • [2] Aguayo, J.; Sánchez, J.: Separable Measures and The Dunford-Pettis Property. Bull. Austral. Math. Soc.. 43, 1991.
  • [3] Khurana, S.S.: Dunford-Pettis Property. J. Math. Anal. Appl.. 65, 1978.
  • [4] Koumoullis, G.: Perfect, µ-additive Measures and Strict Topologies. Illinois J. of Math. 26, N°3, 1982.
  • [5] Sentilles, F.: Bounded continuous functions on a completely regular spaces. Trans. Amer. Math. Soc. 168, 1972.
  • [6] Varadarajan, V.: Measures on topological spaces. Amer. Math. Soc. Transl. 48, 1965.