Weak compactness of almost limited operators

2014/03/13 by Elbour, A., Machrafi, N., Moussa, M.
#46B42 (Primary) 46B50 #47B65 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1403.3348

Abstract

The paper is devoted to the relationship between almost limited operators and weakly compacts 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.

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