This is an announcement for the paper "On quantitative Schur and Dunford-Pettis properties" by Ondrej F.K. Kalenda and Jiri Spurny.

Abstract: We show that the dual to any subspace of $c_0(\Gamma)$ has the strongest possible quantitative version of the Schur property. Further, we establish relationship between the quantitative Schur property and quantitative versions of the Dunford-Pettis property. Finally, we apply these results to show, in particular, that any subspace of the space of compact operators on $\ell_p$ ($1<p<\infty$) with Dunford-Pettis property satisfies automatically both its quantitative versions.

Archive classification: math.FA

Mathematics Subject Classification: 46B25

Remarks: 10 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/1302.6369

or

http://arXiv.org/abs/1302.6369