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<p>In this paper, we establish some necessary and sufficient conditions for generalized <i>n</i>-strong Drazin invertibility (g<i>n</i>s-invertibility) and pseudo <i>n</i>-strong Drazin invertibility (p<i>n</i>s-invertibility) of an element in a Banach algebra for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_811_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\in {\mathbb {N}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math></EquationSource> </InlineEquation>. Subsequently, these results are utilized to prove some additive properties of g<i>n</i>s (p<i>n</i>s)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra <b>70.1</b> (2022): 53-65) for g<i>n</i>s and p<i>n</i>s-Drazin inverse.</p>

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Additive Properties of the generalized and pseudo n-strong Drazin Inverse in Banach Algebras

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Rounak Biswas,
  • Falguni Roy

摘要

In this paper, we establish some necessary and sufficient conditions for generalized n-strong Drazin invertibility (gns-invertibility) and pseudo n-strong Drazin invertibility (pns-invertibility) of an element in a Banach algebra for \(n\in {\mathbb {N}}\) n ∈ N . Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra 70.1 (2022): 53-65) for gns and pns-Drazin inverse.