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

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.