L -DUNFORD–PETTIS PROPERTY IN BANACH SPACES

. Following the concept of Dunford–Pettis sets and Dunford Pettis proeprty in Banach spaces, we introduce the concept of almost L ∗ -Dunford–Pettis sets and L -Dunford–Pettis proeprty in Banach spaces and then we characterize Banach spaces with L ∗ ∗ -Dunford–Pettis proeprty. We obtain some characterizations of them with respect to some well known geometric properties of Banach spaces, such as, Dunford-Pettis property, relatively compact Dunford-Pettis property and Dunford-Pettis completely continuous operators on such Banach spaces.