Work

The Multiplicative Perturbation of Group Invertible Operators in Banach Space

Year: 2026

Type: article

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.

Source: Mathematics

DOI: 10.3390/math14040662

Authors: Saijie Chen, Xiaoli Li, Lanping Zhu, Qianglian Huang

Institutions: Suzhou City University, Yangzhou University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Natural Science Foundation of China, Government of Jiangsu Province