On the Stable Perturbation and Nashed’s Condition for Generalized Inverses

Authors

Jiu Ding, University of Southern MississippiFollow
Qianglian Huang, Yangzhou UniversityFollow

Document Type

Article

Publication Date

1-1-2020

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

© 2020 Taylor & Francis Group, LLC. Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let ¯Τ = Τ + δΤ. Nashed’s condition is that (I + δΤΤ⁺)⁻¹¯Τ maps the null space of T into the range of T. The stable perturbation means that the intersection of the range of ¯Τ and the null space of the generalized inverse of T is {0}. We show that the stable perturbation is the same as Nashed’s condition in the sense of duality.

Publication Title

Numerical Functional Analysis and Optimization

Recommended Citation

Ding, J., Huang, Q. (2020). On the Stable Perturbation and Nashed’s Condition for Generalized Inverses. Numerical Functional Analysis and Optimization.
Available at: https://aquila.usm.edu/fac_pubs/18287