Additive Perturbations and Multiplicative Perturbations for the core inverse of bounded linear operator in Hilbert space

Abstract

In this paper, we present some characteristics and expressions of the core inverse $\core A$ of bounded linear operator $A$
in Hilbert spaces. Additive perturbations of core inverse are investigated under the condition $R(\bar{A})\cap N(A^\#)=\{0\}$
and an upper bound of $\|\core{\bar{A}}-\core A\|$ is obtained. We also discuss the multiplicative perturbations.
The expressions of core inverse of perturbed operator $T=EAF$ and the upper bounds of $\|\core T-\core A\|$ are obtained too.