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DOMINATION BY POSITIVE WEAK
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}^{*}$ DUNFORD–PETTIS OPERATORS ON BANACH LATTICES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 90 / Issue 2 / October 2014
- Published online by Cambridge University Press:
- 05 June 2014, pp. 311-318
- Print publication:
- October 2014
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- Article
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- You have access
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Recently, H’michane et al. [‘On the class of limited operators’, Acta Math. Sci. (submitted)] 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 
$0\leq S\leq T$. We show that if 
$T$ is a weak
$^{*}$ Dunford–Pettis operator and 
$F$ is 
$\sigma $-Dedekind complete, then 
$S$ itself is weak
$^*$ Dunford–Pettis.
