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<p>This paper is devoted to show the stability of generalized Drazin invertible elements relative to a regularity <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R}\)</EquationSource> </InlineEquation> of anti-diagonal matrices in the general case of Banach algebras. Also, it provides a key result in connexion with formulating the generalized Drazin-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {R}\)</EquationSource> </InlineEquation> inverse of a full square block matrix in a Banach algebra. As an example of application, we apply our findings in the setting of bounded linear operators to solve a given second-order partial differential equation.</p>

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A note on block matrices in a Banach algebra and their applications

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Othman Abad,
  • Mbark Abkari,
  • Abdelaziz Tajmouati

摘要

This paper is devoted to show the stability of generalized Drazin invertible elements relative to a regularity \(\mathcal {R}\) of anti-diagonal matrices in the general case of Banach algebras. Also, it provides a key result in connexion with formulating the generalized Drazin- \(\mathcal {R}\) inverse of a full square block matrix in a Banach algebra. As an example of application, we apply our findings in the setting of bounded linear operators to solve a given second-order partial differential equation.