This is an announcement for the paper "Quantitative Dunford-Pettis property" by Miroslav Kacena, Ondrej F.K. Kalenda and Jiri Spurny.

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 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 46B20, 47B07, 47B10

Remarks: 47 pages

Submitted from: kalenda@karlin.mff.cuni.cz

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1110.1243

or

http://arXiv.org/abs/1110.1243