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On weakly compact operators on spaces of vector valued continuous functions

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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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Official URL: http://www.ams.org/journals/proc/1986-097-01/S0002-9939-1986-0831394-3/S0002-9939-1986-0831394-3.pdf


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Abstract

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
Deposited On:07 May 2012 08:37
Last Modified:02 Aug 2018 07:40

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