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<p>This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call <i>DW</i>-DP operators and <i>DW</i>-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that <i>DW</i>-DP (resp. <i>DW</i>-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_429_Article_IEq1.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive <i>DW</i>-DP and positive <i>DW</i>-limited operators are given.</p>

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DW-DP operators and DW-limited operators on Banach lattices

  • 期刊论文

  • 发表日期：

    2025年3月8日

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  • Jin Xi Chen,
  • Jingge Feng

摘要

This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call DW-DP operators and DW-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that DW-DP (resp. DW-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak \(^*\) ∗ Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive DW-DP and positive DW-limited operators are given.