Jerry J. Koliha

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In this paper, we investigate a perturbation of the Drazin inverse AD of a closed linear operator A; the main tool for obtaining the estimates is the gap between subspaces and operators. By (X) we denote the set of all closed linear operators acting on a linear subspace of X to X , where X is a complex Banach space. We write (A), (A), (A), ρ(A), σ(A), and(More)
The paper solves a long standing problem of finding error bounds for a general perturbation of the Drazin inverse. The bounds are given in terms of the distance between the matrices together with the distance between their eigenprojections. Estimates using the gap between subspaces are also given. Recent results of several authors, including Castro, Koliha,(More)
We study perturbations of the Drazin inverse of a closed linear operator A for the case when the perturbed operator has the same spectral projection as A. This theory subsumes results recently obtained by Wei and Wang, Rakočević and Wei, and Castro and Koliha. We give explicit error estimates for the perturbation of Drazin inverse, and error estimates(More)
We study block diagonalization of matrices induced by resolutions of the unit matrix into the sum of idempotent matrices. We show that the block diagonal matrices have disjoint spectra if and only if each idempotent matrix in the inducing resolution double commutes with the given matrix. Applications include a new characterization of an eigenprojection and(More)