Weak Sequential Convergence in the Dual of Compact Operators between Banach Lattices

For several Banach lattices E and F, if K(E; F) denotes the space of all compact operators from E to F, under some conditions on E and F, it is shown that for a closed subspace M of K(E; F), M* has the Schur property if and only if all point evaluations M-1(x) = {Tx : T is an element of M-1} and (M) over tilde (1)(y*) = {T*y* : T is an element of M-1} are relatively norm compact, where x is an element of E, y* is an element of F* and M-1 is the closed unit ball of M.