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Published online by Cambridge University Press:  26 February 2015

Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic email
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic email
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We show that the dual to any subspace of $c_{0}({\rm\Gamma})$ (${\rm\Gamma}$ is an arbitrary index set) has the strongest possible quantitative version of the Schur property. Further, we establish a 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 the Dunford–Pettis property automatically satisfies both its quantitative versions.

Research Article
© 2015 Australian Mathematical Publishing Association Inc. 


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