Geodesic
Another proof of a result of N. J. Kalton, E. Saab and P. Saab on the Dieudonné property in C(K, E)
Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 137-140

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a compact Hausdorff topological space and E be a Banach space not containing l1. Recently N. J. Kalton, E. Saab and P. Saab ([5]) obtained the results that under the above assumptions the usual space C(K, E) has the Dieudonné property; i.e. each weakly completely continuous operator on C(K, E) is weakly compact. They use topological results concerning multivalued mappings in their proof. In this short note we furnish a new and simpler proof of that result without using topological results but only well known theorems of Bourgain ([2]) and Talagrand ([8]) on weak compactness of sets of Bochner integrable functions; i.e. results in vector measure theory. At the end of the paper we present some applications of the result to Banach spaces of compact operators. 
Emmanuele, G. Another proof of a result of N. J. Kalton, E. Saab and P. Saab on the Dieudonné property in C(K, E). Glasgow mathematical journal, Tome 31 (1989) no. 2, pp. 137-140. doi: 10.1017/S0017089500007655
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