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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
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-7317-2351Author: Marjan SHEİBANİ ABDOLYOUSEFİ (Primary Author)Institution: Semnan UniversityCountry: Iran 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 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

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