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Additive perturbations and multiplicative perturbations for the core inverse of bounded linear operator in Hilbert space

Du Fapeng
Nashed Zuhair M.

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( Ā)∩N(A#) = {0} and an upper bound of ||Ā#-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.

Keywords: core inverse, additive perturbations, multiplicative perturbations, gap between subspaces