Quantitative Dunford-Pettis property

الأصل · EN

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 prove that L¹ spaces and C(K) spaces posses both of them. We also show that several natural measures of weak non-compactness are equal in L¹ spaces.