Perturbation for group inverse in a Banach algebra

TL;DR

This paper investigates how the group inverse in a Banach algebra behaves under certain perturbations, providing new additive bounds and extending previous results in the field.

Contribution

It introduces new additive perturbation bounds for the group inverse in Banach algebras, extending prior work with improved upper bounds.

Findings

Derived new bounds for the difference between perturbed and original group inverses

Extended existing perturbation results in Banach algebra context

Provided explicit upper bounds for the norm difference

Abstract

We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of $\|(a+b)^{\#}-a^d\|$ is thereby given. These extend the main results in [X. Liu, Y. Qin and H. Wei, Perturbation bound of the group inverse and the generalized Schur complement in Banach algebra, Abstr. Appl. Anal., 2012, 22 pages. DOI:10.1155/2012/629178].