1. A new perturbation theorem for Moore-Penrose metric generalized inverse of bounded linear operators in Banach spaces
- Author
-
Yuwen Wang and Zi Wang
- Subjects
Unbounded operator ,Discrete mathematics ,Approximation property ,General Mathematics ,010102 general mathematics ,Eberlein–Šmulian theorem ,MathematicsofComputing_NUMERICALANALYSIS ,General Physics and Astronomy ,010103 numerical & computational mathematics ,Finite-rank operator ,Operator theory ,01 natural sciences ,Bounded operator ,0101 mathematics ,C0-semigroup ,Bounded inverse theorem ,Mathematics - 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.
- Published
- 2017