Perfect measures and the dunford-pettis property
Keywords: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.
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