Some remarks on the Dunford-Pettis property

Narcisse Randrianantoanina

Some remarks on the Dunford-Pettis property

Functional Analysis 2009-09-25 v1

Authors: Narcisse Randrianantoanina

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.

Keywords

dunford-pettis property disk algebra compact hausdorff space borel measure dual space

Cite

@article{arxiv.math/9501214,
  title  = {Some remarks on the Dunford-Pettis property},
  author = {Narcisse Randrianantoanina},
  journal= {arXiv preprint arXiv:math/9501214},
  year   = {2009}
}

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