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

Qianglian Huang; Saijie Chen; Lanping Zhu

paper

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

arXiv:1807.01446

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.).