Perfect measures and the dunford-pettis property
Aguayo G., José
Sánchez H., José
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.