On quantitative Schur and Dunford-Pettis properties

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.

14 pages; the paper was enlarged - Section 3 was added

References in corpus (3)

• Quantitative Dunford-Pettis property
• On quantification of weak sequential completeness
• On a difference between quantitative weak sequential completeness and the quantitative Schur property

Cited by in corpus (1)

• Quantitative Schur property and measures of weak non-compactness