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<p>The main content of this paper is to give the conditions containing idempotent elements, under which we calculate the Drazin inverse result of the anti-triangular block matrix containing the identity matrix in Banach space, and then gives the Drazin inverse of the arbitrary anti-triangular block matrix. The above results represent the Drazin inverses for any <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3148_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\times 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> partitioned matrix. The main results of this paper extend some existing results on Drazin inverse. As verification and application, we present examples of the above results.</p>

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Researches on Drazin inverse of operators in Banach space

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • Yu Jin,
  • Daochang Zhang,
  • Chaochao Sun

摘要

The main content of this paper is to give the conditions containing idempotent elements, under which we calculate the Drazin inverse result of the anti-triangular block matrix containing the identity matrix in Banach space, and then gives the Drazin inverse of the arbitrary anti-triangular block matrix. The above results represent the Drazin inverses for any \(2\times 2\) 2 × 2 partitioned matrix. The main results of this paper extend some existing results on Drazin inverse. As verification and application, we present examples of the above results.