Domination by positive weak* Dunford-Pettis operators on Banach lattices

Abstract

Recently, J. H'michane et al. introduced the class of weak* Dunford-Pettis operators on Banach spaces, that is, operators which send weakly compact sets onto limited sets. In this paper the domination problem for weak* Dunford-Pettis operators is considered. Let $S,T:E\to F$ be two positive operators between Banach lattices $E$ and $F$ such that $0\le S\le T$. We show that if $T$ is a weak${}^{\ast }$ Dunford-Pettis operator and $F$ is $\sigma$-Dedekind complete, then $S$ itself is weak* Dunford-Pettis.

8 pages

Cited by in corpus (1)

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