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

TL;DR

This paper studies how small changes in operators affect the stability of a specific generalized inverse on Hilbert spaces, providing conditions, explicit formulas, and bounds for perturbations.

Contribution

It offers new conditions and explicit representations for the stability of $A_{T,S}^{(2)}$ under perturbations in Hilbert spaces.

Findings

Derived explicit perturbation bounds.

Established stability conditions for $A_{T,S}^{(2)}$.

Provided explicit formulas for perturbed operators.

Abstract

In this paper, we investigate the perturbation analysis of $A_{T,S}^{(2)}$ when $T,\,S$ and $A$ have some small perturbations on Hilbert spaces. We present the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable. The explicit representation for the perturbation of $A_{T,S}^{(2)}$ and the perturbation bounds are also obtained.