Weak Compactness of Almost Limited Operators

Abstract EN

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.