A new perturbation theorem for Moore-Penrose metric generalized inverse of bounded linear operators in Banach spaces. Issue 6 (November 2017)

• Record Type: Journal Article
• Authors: WANG, Zi; WANG, Yuwen
• Is Part Of: Acta mathematica scientia. Volume 37:Issue 6(2017)
• Page Start: 1619
• Page End: 1631
• Publication Date: 2017-11
• Subjects: Banach space -- bounded linear operator -- metric projection -- generalized inverse -- perturbation analysis -- Moore-Penrose -- quasi-additive; 47A05; Mathematical physics -- Periodicals; 530.15
• DOI: 10.1016/S0252-9602(17)30095-4
• Languages: English
• ISSNs: 0252-9602

Abstract

Abstract: In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.