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

Authors

  • J. X. Chen Southwest Jiaotong University
  • Z. L. Chen
  • G. X. Ji

Keywords:

limited set, domination property, weak* Dunford-Pettis operator, positive operator, Banach lattice

Abstract

Recently, J. 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 \(S, T:E\rightarrow F\) 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. DOI: 10.1017/S000497271400032X

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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