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Cembranos, Pilar
(1983)
*On Banach-Spaces Of Vector-Valued Continuous-Functions.*
Bulletin Of The Australian Mathematical Society, 28
(2).
pp. 175-186.
ISSN 0004-9727

PDF
Restringido a Repository staff only 366kB |

Official URL: http://journals.cambridge.org/download.php?file=%2FBAZ%2FBAZ28_02%2FS0004972700020852a.pdf&code=2d96bd78

## Abstract

Let K tie a compact Hausdorff space and let E be a Banach

Space. We denote by C(K, E) the Banach space of all E-valued

Continuous functions defined on K , endowed with the supremum Norm.

Recently, Talagrand [Israel J. Math. 44 (1983), 317-321]

Constructed a Banach space E having the Dunford-Pettis property

Such that C([0, l ] , E) fails to have the Dunford-Pettis property.

So he answered negatively a question which was posed some years ago.

We prove in this paper that for a large class of compacts K

(the scattered compacts), C(K, E) has either the Dunford-Pettis

Property, or the reciprocal Dunford-Pettis property, or the

Dieudonne property, or property V if and only if E has the

Same property.

Also some properties of the operators defined on C(K, E) are

Studied.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Mathematics |

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

ID Code: | 14976 |

Deposited On: | 24 Apr 2012 11:39 |

Last Modified: | 13 Jun 2018 08:25 |

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