Weak Compactness of Almost Limited Operators

摘要

This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if is a -Dedekind complete Banach lattice, then every almost limited operator is weakly compact if and only if is reflexive or the norm of is order continuous. Also, we show that if is a -Dedekind complete Banach lattice, then the square of every positive almost limited operator is weakly compact if and only if the norm of is order continuous.