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The Dunford-Pettis
property for certain uniform algebras
Freddy Delbaen |
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Vol. 65 (1976), No. 1, 29–33
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Abstract |
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A Banach space B has the Dunford-Pettis property if xn∗(xn) → 0 whenever xn → 0 weakly and the sequence xn∗ tends to zero weakly in B∗ (i.e. σ(B∗,B∗∗)). Suppose now that A is a uniform algebra on a compact space X. If ϕ is a nonzero multiplicative linear functional on A then Mϕ is the set of positive representing measures of ϕ. If A is such that a singular measure which is orthogonal to A must necessarily be zero and if all Mϕ are weakly compact sets then the algebra A as well as its dual have the Dunford-Pettis property. |
Mathematical Subject Classification 2000
Primary: 46J10
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Milestones
Received: 4 August 1975
Revised: 20 November 1975
Published: 1 July 1976
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Authors |
| Freddy Delbaen | |
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