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 A# of bounded linear operator A in Hilbert spaces. Additive perturbations of core inverse are investigated under the condition R( ?)?N(A#) = {0} and an upper bound of ||?#-A#|| is obtained. We also discuss the multiplicative perturbations. The expressions of core inverse of perturbed operator T = EAF and the upper bounds of ||T#-A#|| are obtained too.