- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 3
- The representations of the g-Drazin inverse in a Banach algebra
The representations of the g-Drazin inverse in a Banach algebra
Authors : Marjan Sheibani Abdolyousefi
Pages : 659-667
Doi:10.15672/hujms.754006
View : 11 | Download : 5
Publication Date : 2021-06-07
Article Type : Research
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