On the Stable Perturbation and Nashed's Condition for Generalized Inverses†. (25th October 2020)

• Record Type: Journal Article
• Authors: Ding, Jiu; Huang, Qianglian
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 14(2020)
• Page Start: 1761
• Page End: 1768
• Publication Date: 2020-10-25
• Subjects: Generalized inverse -- Nashed's condition -- stable perturbation; 47A55 -- 47A05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1813164
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let T ¯ = T + δ T . Nashed's condition is that ( I + δ T T + ) − 1 T ¯ maps the null space of T into the range of T . The stable perturbation means that the intersection of the range of T ¯ 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.