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

Year 2021, Volume: 50 Issue: 3, 659 - 667, 07.06.2021

Marjan Sheibani Abdolyousefi

https://doi.org/10.15672/hujms.754006

Cited By: 9

https://izlik.org/JA33YP69UH

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].

Keywords

g-Drazin inverse , additive property , perturbation , Banach algebra

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