Quantitative Dunford-Pettis property

Details Quantitative Dunford-Pettis property Quantitative Dunford-Pettis property

2011-10-06

arxiv.org/abs/1110.1243v1

Mathematics

Functional Analysis

47 pages

Scientific paper

We investigate possible quantifications of the Dunford-Pettis property. We show, in particular, that the Dunford-Pettis property is automatically quantitative in a sense. Further, there are two incomparable mutually dual stronger versions of a quantitative Dunford-Pettis property. We investigate their relationship with a quantitative Schur property and prove that $L^1$ spaces and $C(K)$ spaces posses both of them. We also show that several natural measures of weak non-compactness are equal in $L^1$ spaces.

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