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.
|Subjects:||Sciences > Mathematics > Mathematical analysis|
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|Deposited On:||07 May 2012 08:37|
|Last Modified:||06 Feb 2014 10:16|
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