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We study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The results include the relation between regular, MP-invertible 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.

We study perturbations and the continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and in terms of the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to… (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, Rakočevi´c and Wei, and Castro and Koliha. We give explicit error estimates for the perturbation of Drazin inverse, and error estimates… (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)

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.

- Jerry J. Koliha
- The American Mathematical Monthly
- 2009

In this paper we use a new approach to obtain a class of multivariable integral inequalities of Hilbert type from which we can recover as special cases integral inequalities obtained recently by Pachpatte and the present authors.

We study semi-iterative methods for an approximate solution of a linear equation x = T x+c with a bounded linear operator T acting on a Banach space X, considering separately the cases when λ = 1 is an isolated and accumulation spectral point for T. We give necessary and sufficient conditions for the convergence of a semi-iterative method, utilizing the… (More)

- Jerry J. Koliha
- The American Mathematical Monthly
- 2006

This paper presents a class of L p-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)