Weak Dunford-Pettis Property for a Closed Sublattice of Compact Operators

For several Banach lattices E and F, if K(E, F) denotes the space of all compact operators from E to F, it is shown that a necessary and sufficient condition for a closed subspaceMof K(E, F) to have the weak Dunford–Pettis property is that all evaluation operators ʹx :M! F and y :M! E are almost Dunford–Pettis operators, where ʹx(T) = Tx and y (T) = Ty for x 2 E, y 2 F and T 2M.