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<p>A subclass of weak Dunford–Pettis operators named <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_454_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {w}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>w</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>DP operators is under investigation. The article studies conditions under which <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_454_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {w}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>w</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>DP-operators have properties such as (weak) compactness and limitedness, and the relationship of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_454_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbox {w}^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>w</mtext> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>DP operators with Dunford–Pettis operators. Several further topics related to these operators are investigated.</p>

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On \(\hbox {w}^*\)-Dunford–Pettis operators

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Şafak Alpay,
  • Svetlana Gorokhova

摘要

A subclass of weak Dunford–Pettis operators named \(\hbox {w}^*\) w ∗ DP operators is under investigation. The article studies conditions under which \(\hbox {w}^*\) w ∗ DP-operators have properties such as (weak) compactness and limitedness, and the relationship of \(\hbox {w}^*\) w ∗ DP operators with Dunford–Pettis operators. Several further topics related to these operators are investigated.