The paper is devoted to the relationship between almost limited operators and
weakly compacts operators. We show that if F is a Ο-Dedekind complete
Banach lattice then, every almost limited operator T:EβF is
weakly compact if and only if E is reflexive or the norm of F is order
continuous. Also, we show that if E is a Ο-Dedekind complete Banach
lattice then the square of every positive almost limited operator T:EβE is weakly compact if and only if the norm of E is order
continuous.Comment: 5 page