Quantitative Dunford-Pettis property

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 possess both of them. We also show that several natural measures of weak non-compactness are equal in L1 spaces.