### Impacto

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 |

References: | F. Bombai and P. Cembranos, Characterization of some classes of operators on spaces of vector-valued continuous functions. Math. Proc. Cambridge Philos. Soc. 97 (1985), 137-146. F. Bombai and B. Rodriguez-Salinas, Some classes of operators on C(K,E). Extension and applications. Arch. Math, (to appear). I. K. Brooks and P. W. Lewis, Linear operators and vector measures. Trans. Amer. Math. Soc. 192 (1974), 139-162. P. Cembranos, On Banach spaces of vector valued continuous functions, Bull. Austral. Math. Soc. 28 (1983). 175-186. I. Diestel, A survey of results related to the Dunford-Pettis property, Proc. Conf. on Integration, Topology and Geometry in Linear Spaces, Contemporary Math., vol. 2, Amer. Math. Soc, Providence, R.I.. 1975. I. Diestel and I. I. Uhl, Ir., Vector measures, Math. Surveys, no. 15. Amer. Math. Soc, Providence, R.I.. 1977. I. Dobrakov, On representation of linear operators on C0(T, X), Czechoslovak Math. I. 21 (1971), 13-30. A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C( K ), Canad. J. Math. 5(1953), 129-173 J. Horvath. Topological vector spaces und distributions, Addison-Wesley, Reading, Mass.. 1966. H. E. Lacey. 77;e isometric theory of classical Banach spaces. Springer. Berlin, 1974. L. Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press. London. 1973. M. Talagrand. La propriété de Dunford-Pettis dans C(K, E) et Ll(E), Israel J. Math. 44 (1983). 317-321. |

Deposited On: | 07 May 2012 08:37 |

Last Modified: | 06 Feb 2014 10:16 |

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