Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces

TL;DR

This paper investigates how bounded homogeneous and quasi-linear projector generalized inverses of bounded linear operators on Banach spaces respond to perturbations, extending known results for linear operator inverses.

Contribution

It introduces the study of perturbation problems for bounded homogeneous and quasi-linear projector generalized inverses, extending classical results to these broader inverse types.

Findings

Extended perturbation analysis to bounded homogeneous generalized inverses

Provided applications to Moore--Penrose metric generalized inverse

Generalized classical results for linear operator inverses

Abstract

Let $X, Y$ be Banach spaces and $T : X \to Y$ be a bounded linear operator. In this paper, we initiate the study of the perturbation problems for bounded homogeneous generalized inverse $T^h$ and quasi--linear projector generalized inverse $T^H$ of $T$. Some applications to the representations and perturbations of the Moore--Penrose metric generalized inverse $T^M$ of $T$ are also given. The obtained results in this paper extend some well--known results for linear operator generalized inverses in this field.