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arXiv · 1110.1243

Quantitative Dunford-Pettis property

Miroslav Kačena·Ondřej F. K. Kalenda·Jiří Spurný
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Abstract

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 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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Miroslav Kačena, Ondřej F. K. Kalenda, Jiří Spurný. 2012-11-19. Quantitative Dunford-Pettis property. https://doi.org/10.1016/j.aim.2012.10.019

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