Weak compactness of almost limited operators

This paper is devoted to the relationship between almost limited operators and weakly compact operators. we show that if f is a σ-dedekind complete banach lattice,then every almost limited operator t : e → f 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 σ-dedekind complete banach lattice,then the square of every positive almost limited operator t : e → e is weakly compact if and only if the norm of e is order continuous. copyright © 2014 aziz elbour et al.