Weak Compactness of Almost Limited Operators. (2nd December 2014) - Elbour, Aziz; Machrafi, Nabil; Moussa, Mohammed
Abstract : This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that ifF is aσ -Dedekind complete Banach lattice, then every almost limited operatorT : E → F is weakly compact if and only ifE is reflexive or the norm ofF is order continuous. Also, we show that ifE is aσ -Dedekind complete Banach lattice, then the square of every positive almost limited operatorT : E → E is weakly compact if and only if the norm ofE is order continuous.