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 A # of bounded linear operator A in Hilbert spaces. Additive perturbations of core inverse are investigated under the condition R(¯ A)∩N(A #) = {0} and an upper bound of ¯ A # −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.