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Abstract <p>It is shown that the set of all <i>C</i>-compact orthogonally additive operators from a vector lattice <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10466_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E\)</EquationSource> <!--RusMath2570011Dzhusoeva-m1--> </InlineEquation> to an <i>AM</i>-space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10466_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(F\)</EquationSource> <!--RusMath2570011Dzhusoeva-m2--> </InlineEquation> is a vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. Moreover, a positive <i>AM</i>-compact orthogonally additive map defined on a lateral ideal of a vector lattice <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10466_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E\)</EquationSource> <!--RusMath2570011Dzhusoeva-m3--> </InlineEquation> and taking values in an <i>AM</i>-space <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10466_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(F\)</EquationSource> <!--RusMath2570011Dzhusoeva-m4--> </InlineEquation> can be extended to the whole space <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11982_2025_10466_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(E\)</EquationSource> <!--RusMath2570011Dzhusoeva-m5--> </InlineEquation>.</p>

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On C-Compact Orthogonally Additive Operators

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • N. A. Dzhusoeva,
  • Z. S. Valgasov

摘要

Abstract

It is shown that the set of all C-compact orthogonally additive operators from a vector lattice \(E\) to an AM-space \(F\) is a vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. Moreover, a positive AM-compact orthogonally additive map defined on a lateral ideal of a vector lattice \(E\) and taking values in an AM-space \(F\) can be extended to the whole space \(E\) .