Perturbation analysis of $A_{T,S}^{(2)}$ on Banach spaces

TL;DR

This paper investigates the stability of the generalized inverse $A_{T,S}^{(2)}$ in Banach spaces under perturbations, providing explicit formulas and bounds to understand how small changes affect it.

Contribution

It introduces new conditions and explicit formulas for the perturbation bounds of $A_{T,S}^{(2)}$ in Banach spaces, enhancing understanding of its stability.

Findings

Derived conditions for stability under perturbations

Obtained explicit formulas for perturbation of $A_{T,S}^{(2)}$

Established new bounds for perturbation effects

Abstract

In this paper, the perturbation problems of $A_{T,S}^{(2)}$ are considered. By virtue of the gap between subspaces, we derive the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable when $T,S$ and $A$ have suitable perturbations. At the same time, the explicit formulas for perturbation of $A_{T,S}^{(2)}$ and new results on perturbation bounds are obtained.