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ON QUANTITATIVE SCHUR AND DUNFORD–PETTIS PROPERTIES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 91 / Issue 3 / June 2015
- Published online by Cambridge University Press:
- 26 February 2015, pp. 471-486
- Print publication:
- June 2015
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- Article
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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.
