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On weakly compact operators on spaces of vector valued continuous functions


Bombal Gordón, Fernando (1986) On weakly compact operators on spaces of vector valued continuous functions. Proceedings of the American Mathematical Society , 97 (1). pp. 93-96. ISSN 0002-9939

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Let K and S be compact Hausdorff spaces and 8 a continuous function from K onto S. Then for any Banach space E the map / -» / ° 9 isometrically embeds C(S, £) as a closed subspace of C(K, E). In this note we prove that when E' has the Radon-Nikodym property, every weakly compact operator on C(S, E) can be lifted to a weakly compact operator on C( K, E). As a consequence, we prove that the compact dispersed spaces K are characterized by the fact that C(K, E) has the Dunford-Pettis property whenever E has.

Item Type:Article
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15111

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