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Dergiler / 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
Sayfa
659–667
Yayın Tarihi
2022-10-18
DOI
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Comput. 218, 10226-10237, 2012] and Dopazo and Martinez-Serano [Linear Algebra Appl. 432, 1896-1904, 2010].

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:These extend the results on Drazin inverse of Bu, Feng and Bai [Appl.
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Sonuç & Katkı:Comput. 218, 10226-10237, 2012] and Dopazo and Martinez-Serano [Linear Algebra Appl. 432, 1896-1904, 2010].
🔬Tür:Araştırma Makalesi
📍Kapsam:2012 Verileri
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (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
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  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.