Perfect measures and the dunford-pettis property


  • José Aguayo G. Universidad de Concepción.
  • José Sánchez H. Universidad de Concepción.



Perfect measures, Strict topologies, Dunford-Pettis Property


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 ?p 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 ?-continuous on Cb(X), where E denotes a Banach space. We also prove that (Cb(X),( ?p) has strict Dunford-Pettis property and, if X contains a ?-compact dense subset, (Cb(X), ?p) has Dunford-Pettis property.

Author Biographies

José Aguayo G., Universidad de Concepción.

Departamento de Matemática.

José Sánchez H., Universidad de Concepción.

Departamento de Matemática.


[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.



How to Cite

J. Aguayo G. and J. Sánchez H., “Perfect measures and the dunford-pettis property”, Proyecciones (Antofagasta, On line), vol. 11, no. 2, pp. 125-129, Apr. 2018.




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