Some remarks on the Dunford-Pettis property

Abstract

Let $A$ be the disk algebra, $\Omega$ be a compact Hausdorff space and $\mu$ be a finite Borel measure in $\Omega$. It is shown that the dual of $C(\Omega,A)$ has the Dunford-Pettis Property. This proved in particular that the spaces $C(\Omega,A)$ and $L^1(\mu,A*)$ have the Dunford-Pettis property.