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<p>We introduce and explore the concept of positive ideals for both linear and multilinear operators between Banach lattices. This paper delineates the fundamental principles of these new classes and provides techniques for constructing positive multi-ideals from given positive ideals. Furthermore, we present an example of a positive multi-ideal by introducing a new class, referred to as positive <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11117_2025_1112_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="92" /> </InlineMediaObject> <EquationSource Format="TEX">\((p_{1},...,p_{m};r)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>p</mi> <mi>m</mi> </msub> <mo>;</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dominated multilinear operators. We establish a natural analogue of the Pietsch domination theorem and Kwapień’s factorization theorem within this class.</p>

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Positive ideals of multilinear operators

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • Athmane Ferradi,
  • Abdelaziz Belaada,
  • Khalil Saadi

摘要

We introduce and explore the concept of positive ideals for both linear and multilinear operators between Banach lattices. This paper delineates the fundamental principles of these new classes and provides techniques for constructing positive multi-ideals from given positive ideals. Furthermore, we present an example of a positive multi-ideal by introducing a new class, referred to as positive \((p_{1},...,p_{m};r)\) ( p 1 , . . . , p m ; r ) -dominated multilinear operators. We establish a natural analogue of the Pietsch domination theorem and Kwapień’s factorization theorem within this class.