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<p>In this paper, we use general operational quantities in order to introduce a new class of operators <i>F</i>(<i>X</i>,&#xa0;<i>Y</i>) equivalent to the set of generalized Fredholm operators <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1304_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Psi (X, Y )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ψ</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Moreover we give some topological structures and properties of the set. Lastly we give some properties to operators using a comparison between two operational quantities.</p>

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A general fredholm theory and normal operational quantity

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Aymen Ammar,
  • Abdessattar Lafi

摘要

In this paper, we use general operational quantities in order to introduce a new class of operators F(X, Y) equivalent to the set of generalized Fredholm operators \(\Psi (X, Y )\) Ψ ( X , Y ) . Moreover we give some topological structures and properties of the set. Lastly we give some properties to operators using a comparison between two operational quantities.