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- Jerry J. Koliha
- 2008

In this paper we define and study a generalized Drazin inverse x for ring elements x, and give a characterization of elements a, b for which aa = bb. We apply our results to the study of EP elements in a ring with involution. 2000 Mathematics subject classification: primary 16A32, 16A28, 15A09; secondary 46H05, 46L05.

We study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The results include the relation between regular, MPinvertible and well-supported elements. We present an algebraic proof of the reverse order rule for the MP-inverse valid under certain conditions on MP-invertible elements. Applications to C∗-algebras are given. 2000… (More)

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)

- Jerry J. Koliha
- Applied Mathematics and Computation
- 2002

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)

In this paper we continue our investigation of multivariable integral inequalities of the type considered by Hilbert and recently by Pachpatte by focusing on fractional derivatives. Our results apply to integrable not necessarily continuous functions, and we are able to relax the original conditions to admit negative exponents in the weight functions.… (More)

This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor’s formula, which enables us to relax… (More)

- Jerry J. Koliha
- 2002

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)

If A(z) is a function of a real or complex variable with values in the space B(X) of all bounded linear operators on a Banach space X with each A(z) g-Drazin invertible, we study conditions under which the g-Drazin inverse AD(z) is differentiable. From our results we recover a theorem due to Campbell on the differentiability of the Drazin inverse of a… (More)