Perturbation analysis for Moore-Penrose inverse of closed operators on Hilbert spaces

TL;DR

This paper studies how small changes in closed operators on Hilbert spaces affect their Moore-Penrose inverses, providing new formulas and bounds that extend existing results.

Contribution

It introduces a new inner product to derive explicit expressions and bounds for the Moore-Penrose inverse under perturbations of closed operators on Hilbert spaces.

Findings

Derived explicit formulas for perturbed Moore-Penrose inverses.

Established upper bounds for the norms of inverse and their differences.

Extended and improved existing perturbation results in the literature.

Abstract

In this paper, we investigate the perturbation for the Moore-Penrose inverse of closed operators on Hilbert spaces. By virtue of a new inner product defined on $H$, we give the expression of the Moore-Penrose inverse $\bar{T}^\dag$ and the upper bounds of $\|\bar{T}^\dag\|$ and $\|\bar{T}^\dag -T^\dag\|$. These results obtained in this paper extend and improve many related results in this area.