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<p>Our purpose in this paper is to explain how to calculate the relative homology corresponding to an operator ideal, presenting the raw Banach space facts as well as their homological translations. We will display a few extremal cases to show how different the standard derivation (relative to the operator ideal <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak L\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">L</mi> </math></EquationSource> </InlineEquation> of all linear bounded maps) and relative derivation with respect to an operator ideal <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak A\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">A</mi> </math></EquationSource> </InlineEquation> can be.</p>

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Derivation of operator ideals in Banach spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月15日

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  • Jesús M. F. Castillo,
  • Ricardo García,
  • Yolanda Moreno Salguero

摘要

Our purpose in this paper is to explain how to calculate the relative homology corresponding to an operator ideal, presenting the raw Banach space facts as well as their homological translations. We will display a few extremal cases to show how different the standard derivation (relative to the operator ideal \(\mathfrak L\) L of all linear bounded maps) and relative derivation with respect to an operator ideal \(\mathfrak A\) A can be.