Year 2021, Volume 50 , Issue 3, Pages 659 - 667 2021-06-07

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

Marjan SHEİBANİ ABDOLYOUSEFİ [1]


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].
g-Drazin inverse, additive property, perturbation, Banach algebra
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-7317-2351
Author: Marjan SHEİBANİ ABDOLYOUSEFİ (Primary Author)
Institution: Semnan University
Country: Iran


Dates

Publication Date : June 7, 2021

Bibtex @research article { hujms754006, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {659 - 667}, doi = {10.15672/hujms.754006}, title = {The representations of the g-Drazin inverse in a Banach algebra}, key = {cite}, author = {Sheibani Abdolyousefi, Marjan} }
APA Sheibani Abdolyousefi, M . (2021). The representations of the g-Drazin inverse in a Banach algebra . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 659-667 . DOI: 10.15672/hujms.754006
MLA Sheibani Abdolyousefi, M . "The representations of the g-Drazin inverse in a Banach algebra" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 659-667 <https://dergipark.org.tr/en/pub/hujms/issue/62731/754006>
Chicago Sheibani Abdolyousefi, M . "The representations of the g-Drazin inverse in a Banach algebra". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 659-667
RIS TY - JOUR T1 - The representations of the g-Drazin inverse in a Banach algebra AU - Marjan Sheibani Abdolyousefi Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.754006 DO - 10.15672/hujms.754006 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 659 EP - 667 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.754006 UR - https://doi.org/10.15672/hujms.754006 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics The representations of the g-Drazin inverse in a Banach algebra %A Marjan Sheibani Abdolyousefi %T The representations of the g-Drazin inverse in a Banach algebra %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.754006 %U 10.15672/hujms.754006
ISNAD Sheibani Abdolyousefi, Marjan . "The representations of the g-Drazin inverse in a Banach algebra". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 659-667 . https://doi.org/10.15672/hujms.754006
AMA Sheibani Abdolyousefi M . The representations of the g-Drazin inverse in a Banach algebra. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 659-667.
Vancouver Sheibani Abdolyousefi M . The representations of the g-Drazin inverse in a Banach algebra. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 659-667.
IEEE M. Sheibani Abdolyousefi , "The representations of the g-Drazin inverse in a Banach algebra", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 659-667, Jun. 2021, doi:10.15672/hujms.754006