### Impacto

Cembranos Diaz, Pilar
(1984)
*The Hereditary Dunford-Pettis Property On C(K,E).*
Illinois Journal of Mathematics, 91
(4).
pp. 556-558.
ISSN 0019-2082

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Official URL: http://projecteuclid.org/euclid.ijm/1256069289

## Abstract

The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if one of the following holds: (a) K is finite andX has the hereditary Dunford-Pettis property; (b) C(K) and c0(X) have the hereditary Dunford-Pettis property. Unwilling to give up here, the author provides an elegant characterization of when c0(X) has the hereditary Dunford-Pettis property. Since the paper was written, Nunez has provided an elegant example (based on work of Talagrand) of an X such that, while X is hereditarily Dunford-Pettis, c0(X) is not. Remarkable and satisfying!

Item Type: | Article |
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Uncontrolled Keywords: | Mathematics; Applied; Mathematics |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 14953 |

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Deposited On: | 24 Apr 2012 10:39 |

Last Modified: | 06 Feb 2014 10:12 |

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