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<p>We study the bilinear functor <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak B\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">B</mi> </math></EquationSource> </InlineEquation> that associates to a Banach space <i>X</i> the Banach space <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak B(X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="fraktur">B</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of scalar bilinear bounded forms on <i>X</i>. We obtain its injective and projective derivatives, compute its projective and injective stabilization and introduce and compute its coprojective and coinjective stabilizations.</p>

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Bilinear Derivation in Banach Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月12日

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  • Jesús M. F. Castillo,
  • Ricardo García

摘要

We study the bilinear functor \(\mathfrak B\) B that associates to a Banach space X the Banach space \(\mathfrak B(X)\) B ( X ) of scalar bilinear bounded forms on X. We obtain its injective and projective derivatives, compute its projective and injective stabilization and introduce and compute its coprojective and coinjective stabilizations.