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

## 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 |
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Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 15111 |

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Deposited On: | 07 May 2012 08:37 |

Last Modified: | 06 Feb 2014 10:16 |

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