The Multiplicative Perturbation of Group Invertible Operators in Banach Space
Abstract
In this paper, the multiplicative perturbation of group invertible operators is studied. We first establish necessary and sufficient conditions for the existence, along with explicit expressions, of the group inverse under multiplicative perturbation. Building on these results, we analyze the continuity of multiplicative perturbation and derive perturbation bounds for the group inverse. Furthermore, we extend our study to the group invertibility of linear combinations of operators.
Fields of Study & Subjects
Advanced Banach Space Theory
Matrix Theory and Algorithms
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 4
- Pages
- 662–662
- Publication date
- 13 February 2026
- Language
- EN