A Dunford-Pettis theorem for |
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Authors: | I Cnop F Delbaen |
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Affiliation: | Departement Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium |
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Abstract: | The spaces in the title are associated to a fixed representing measure m for a fixed character on a uniform algebra. It is proved that the set of representing measures for that character which are absolutely continuous with respect to m is weakly relatively compact if and only if each m-negligible closed set in the maximal ideal space of L∞ is contained in an m-negligible peak set for H∞. J. Chaumat's characterization of weakly relatively compact subsets in therefore remains true, and is complete, under the first conditions. In this paper we also give a direct proof. From this we obtain that has the Dunford-Pettis property. |
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