Abstract
In this paper, we investigate some additive results on g$\pi$-Hirano invertibility in Banach algebras. By applying our results, some new results for operator matrices are obtained. This extends the main results of [H. Zou, T. Li and Y. Wei, arXiv:2302.06080v1].
Publisher
The International Electronic Journal of Algebra
Reference14 articles.
1. N. Castro Gonzalez and J. J. Koliha, New additive results for the g-Drazin inverse, Proc. Roy. Soc. Edinburgh Sect. A, 134 (2004), 1085-1097.
2. H. Chen and M. Sheibani, The g-Hirano inverse in Banach algebras, Linear Multilinear Algebra, 69 (2021), 1352-1362.
3. H. Chen and M. Sheibani, Jacobson's Lemma for the generalized n-strongly Drazin inverse, arXiv: 2001.00328v2 [math.RA].
4. D. S. Cvetkovic-Ilic, D. S. Djordjevic and Y. Wei, Additive results for the generalized Drazin inverse in a Banach algebra, Linear Algebra Appl., 418 (2006), 53-61.
5. D. S. Cvetkovic-Ilic, X. Liu and Y. Wei, Some additive results for the generalized Drazin inverse in a Banach algebra, Electron. J. Linear Algebra, 22 (2011), 1049-1058.