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Spaces of vector-valued continuous functions with the Dunford-Pettis property. (Spanish: Espacios de funciones continuas vectoriales con la propiedad de Dunford-Pettis).

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Bombal Gordón, Fernando (1986) Spaces of vector-valued continuous functions with the Dunford-Pettis property. (Spanish: Espacios de funciones continuas vectoriales con la propiedad de Dunford-Pettis). Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, 80 (4). pp. 607-608. ISSN 0034-0596

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Abstract

A Banach space E has the Dunford-Pettis property (D.P.P.) if for every pair of sequences(x n ) in E and (x ′n ) in E ′, both weakly convergent to zero, we have that (x′n (x n )) tends to zero. P. Cembranos [Bull. Austral. Math. Soc. 28 (1983), no. 2, 175–186;] has proved that, if K is a compact Hausdorff dispersed space, then the following holds: For every Banach E with the D.P.P., the Banach space C(K,E) of continuous functions from K into E has the D.P.P.
In the note under review the author proves that this property characterizes compact dispersed spaces.


Item Type:Article
Uncontrolled Keywords:Banach spaces;Dunford-Pettis property
Subjects:Sciences > Mathematics > Differential geometry
ID Code:18125
Deposited On:01 Feb 2013 12:17
Last Modified:02 Aug 2018 07:43

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