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Researches on Drazin inverse of operators in Banach space

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Abstract

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 \(2\times 2\) 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.

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Acknowledgements

Research supported by the National Natural Science Foundation of China (NSFC) (No. 12171213; No. 11901079), and China Postdoctoral Science Foundation (No. 2021M700751). Scientific and Technological Research Program Foundation of Jilin Province: (No. JJKH20250851KJ).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Lanzhou University, Lanzhou, People’s Republic of China

    Yu Jin

  2. College of Sciences, Northeast Electric Power University, Jilin, People’s Republic of China

    Daochang Zhang

  3. College of Mathematics and Statistics, Linyi University, Linyi, People’s Republic of China

    Chaochao Sun

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  1. Yu Jin
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  2. Daochang Zhang
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  3. Chaochao Sun
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Correspondence to Daochang Zhang.

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Jin, Y., Zhang, D. & Sun, C. Researches on Drazin inverse of operators in Banach space. Comp. Appl. Math. 44, 202 (2025). https://doi.org/10.1007/s40314-025-03148-4

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  • DOI: https://doi.org/10.1007/s40314-025-03148-4

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