Weak Dunford--Pettis property for closed sublattices

For several Banach lattices E and F, if K(E; F) de- notes the space of all compact operators from E to F, it is shown that a necessary and su_x000E_cient condition for a closed subspace M of K(E; F) to have the weak Dunford{Pettis property is that all evaluation operators x : M ! F and y_x0003_ : M ! E_x0003_ are almost Dunford{Pettis operators, where x(T) = Tx and y_x0003_ (T) = T_x0003_y_x0003_ for x 2 E, y_x0003_ 2 F_x0003_ and T 2 M.