Abstract
We obtain two different expressions for the weighted core–EP inverse of the sum \(A+E\) for a given operator A and a perturbation operator E, under different conditions on the perturbing operator. As a consequence of these results, we get some relations between idempotents determined by the weighted core–EP inverses of a given operator and its perturbation and we present perturbation bounds for the weighted core–EP inverse. The application to the solution of a perturbed equation is given. We also apply these results to obtain perturbation results for the core–EP inverse.
Similar content being viewed by others
References
Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58(6), 681–697 (2010)
Cao, J., Xue, Y.: Perturbation analysis of the Moore–Penrose metric generalized inverse with applications. Banach J. Math. Anal. 12(3), 709–729 (2018)
Castro González, N., Koliha, J.J.: New additive results for the \(g\)-Drazin inverse. Proc. R. Soc. Edinb. Sect. A 134, 1085–1097 (2004)
Dajić, A., Koliha, J.J.: The weighted g-Drazin inverse for operators. J. Austr. Math. Soc. 82, 163–181 (2007)
Ferreyra, D.E., Levis, F.E., Thome, N.: Revisiting the core EP inverse and its extension to rectangular matrices. Quaest. Math. 41(2), 265–281 (2018)
Koliha, J.J.: A generalized Drazin inverse. Glasg. Math. J. 38, 367–381 (1996)
Ma, H.: Optimal perturbation bounds for the core inverse. Appl. Math. Comput. 336, 176–181 (2018)
Mosić, D.: Weighted core-EP inverse of an operator between Hilbert spaces. Linear Multilinear Algebra 67(2), 278–298 (2019)
Mosić, D., Djordjević, D.S.: The gDMP inverse of Hilbert space operators. J. Spectr. Theor. 8(2), 555–573 (2018)
Mosić, D., Zou, H., Chen, J.: The generalized Drazin inverse of the sum in a Banach algebra. Ann. Funct. Anal. 8(1), 90–105 (2017)
Prasad, K.M., Mohana, K.S.: Core–EP inverse. Linear Multilinear Algebra 62(6), 792–802 (2014)
Rakočević, V., Wei, Y.: A weighted Drazin inverse and applications. Linear Algebra Appl. 350(1–3), 25–39 (2002)
Wei, Y., Wang, G.: The perturbation theory for the Drazin inverse and its applications. Linear Algebra Appl. 258, 179–186 (1997)
Wei, Y., Woo, C.W., Lei, T.: A note on the perturbation of the W-weighted Drazin inverse. Appl. Math. Comput. 149, 423–430 (2004)
Xu, Z., Wang, G.: The representation and perturbation of the \(W\)-weighted Drazin inverse. J. Appl. Math. Comput. 23(1–2), 113–126 (2007)
Acknowledgements
The author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, grant no. 174007. The authors is grateful to the referee for careful reading of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Ilya M. Spitkovsky.
Rights and permissions
About this article
Cite this article
Mosić, D. Perturbation of the weighted core–EP inverse. Ann. Funct. Anal. 11, 75–86 (2020). https://doi.org/10.1007/s43034-019-00022-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s43034-019-00022-3