Weak Compactness of Almost Limited Operators. (2nd December 2014)

• Record Type: Journal Article
• Authors: Elbour, Aziz; Machrafi, Nabil; Moussa, Mohammed
• Other Names: Gao Ji Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-12-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/263159
• Languages: English
• ISSNs: 2314-8896

Abstract

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.