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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

The representations of the g-Drazin inverse in a Banach algebra

Marjan SHEIBANI ABDOLYOUSEF
Pages
659–667
Publication Date
2022-10-18
DOI
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⚡ TL;DR(Too Long; Didn't Read)

Comput. 218, 10226-10237, 2012] and Dopazo and Martinez-Serano [Linear Algebra Appl. 432, 1896-1904, 2010].

📌 3 Key Takeaways

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Objective & Hypothesis:The aim of this paper is to establish an explicit representation of the generalized Drazin inverse $(a+b)^d$ under the condition $$ab^2=0, ba^2=0, a^{\pi}b^{\pi}(ba)^2=0.$$ Furthermore, we apply our results to give some representation of generalized Drazin inverse for a $2\times 2$ block operator matrix.
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Key Findings & Data:These extend the results on Drazin inverse of Bu, Feng and Bai [Appl.
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Conclusion & Impact:Comput. 218, 10226-10237, 2012] and Dopazo and Martinez-Serano [Linear Algebra Appl. 432, 1896-1904, 2010].
🔬Design:Research Article
📍Scope:2012 Verileri
⚙️Variables:g-Drazin inverse · additive property · perturbation

Abstract

The aim of this paper is to establish an explicit representation of the generalized Drazin inverse $(a+b)^d$ under the condition $$ab^2=0, ba^2=0, a^{\pi}b^{\pi}(ba)^2=0.$$ Furthermore, we apply our results to give some representation of generalized Drazin inverse for a $2\times 2$ block operator matrix. These extend the results on Drazin inverse of Bu, Feng and Bai [Appl. Math. Comput. 218, 10226-10237, 2012] and Dopazo and Martinez-Serano [Linear Algebra Appl. 432, 1896-1904, 2010].

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Cite This Article

ABDOLYOUSEF, M. S. (2022). The representations of the g-Drazin inverse in a Banach algebra. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 659–667. https://ajindex.com/articles/530003

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References (11)

  1. J. Benítez, X. Qin and X. Liu, New additive results for the generalized Drazin inverse in a Banach Algebra, Filomat 30 (8), 2289-2294, 2016
  2. C. Bu, C. Feng and S. Bai, Representations for the Drazin inverses of the sum of two matrices and some block matrices, Appl. Math. Comput. 218, 10226-10237, 2012
  3. S. Campbell, The Drazin inverse and systems of second order linear differential equations, Linear Multilinear Algebra 14, 195-198, 1983
  4. S.L. Campbell and C.D. Meyer, Generalized inverses of linear transformations, SIAM, 2009
  5. N. Castro-González and J.J. Koliha, New additive results for the G- Drazin inverse, Proc. Roy. Soc. Edinburgh. Sect A, 134, 1084-1097, 2004
  6. C. Deng, D.S. Cvetcović-Ilić and Y. Wei, Some results on the genrealized Derazin inverse of operator matrices, Linear Multilinear Algebra 58, 503-521, 2010
  7. E. Dopazo and M.F. Martinez-Serrano, Further results on the representation of the Drazin inverse of a $2\times2$ block matrix, Linear Algebra Appl., 432, 1896-1904, 2010
  8. Y. Liao, J. Chen and J. Cui, Cline’s formula for the generalized Drazin inverse, Bull. Malays. Math. Sci. Soc. 37, 37–42, 2014
  9. D. Mosić and D.S. Djordjević, Block representations of the generalized Drazin inverse, Appl. Math. Comput. 331, 200-209, 2018
  10. H. Yang and X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Applied Math. 235, 1412-1417, 2011
  11. X. Zhang and G. Chen, The computation of Drazin inverse and its applications in Markov chains, Appl. Math. Comput. 183, 292-300, 2006.