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

Fapeng Du, M.Zuhair Nashed


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.


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