DP1 and completely continuous operators

Elizabeth M. Bator and Dawn R. Slavens

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-4

Abstract:

W. Freedman introduced an alternate to the Dunford-Pettis property, called the DP1 property, in 1997. He showed that for 1 ≤ p < ∞ , ( ⊕ α ∈ 𝒜 X α ) p has the DP1 property if and only if each X α does. This is not the case for ( ⊕ α ∈ 𝒜 X α ) ∞ . In fact, we show that ( ⊕ α ∈ 𝒜 X α ) ∞ has the DP1 property if and only if it has the Dunford-Pettis property. A similar result also holds for vector-valued continuous function spaces.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:737280

DOI: 10.1155/S0161171203302315

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