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A Dunford-Pettis theorem forL 1 H ∞⊥

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
24
Issue
4
Identifiers
DOI: 10.1016/0022-1236(77)90064-7
Disciplines
  • Mathematics

Abstract

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 L 1 H ∞⊥ therefore remains true, and L 1 H ∞⊥ is complete, under the first conditions. In this paper we also give a direct proof. From this we obtain that L 1 H ∞⊥ has the Dunford-Pettis property.

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