On the perturbation and expression for the core inverse of linear operator in Hilbert space

TL;DR

This paper investigates conditions under which the core inverse of a perturbed linear operator in a Hilbert space can be expressed in a simplified form, improving upon recent perturbation bounds.

Contribution

It provides new necessary and sufficient conditions for the simplified expression of the core inverse under perturbations, advancing the theoretical understanding.

Findings

Derived conditions for the core inverse of perturbed operators

Improved perturbation bounds compared to previous work

Simplified expressions for the core inverse in Hilbert spaces

Abstract

In this note, we provide some sufficient and necessary conditions for the core inverse of the perturbed operator to have the simplest possible expression. The results improve the recent work by H. Ma (Optimal perturbation bounds for the core inverse, Appl. Math. Comput. 336 (2018) 176-181.).