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 $L^1$ spaces and $C(K)$ spaces posses both of them. We also show that several natural measures of weak non-compactness are equal in $L^1$ spaces. 
Miroslav Ka\v{c}ena, Ond\v{r}ej F. K. Kalenda and Ji\v{r}\'i Spurn\'y
math.FA