Keywords: Drazin inverse Anti-triangular operator matrix Resolvent expansion a b s t r a c t This paper deals with the anti-triangular operator matrix M ¼ A B C 0 with A 2 ¼ A and CA p B ¼ 0. Using the resolvent expansion technique, we obtain the explicit representation of the Drazin inverse of M, in terms of its entries and the Drazin inverses of the entries and their compositions. The result ...

We present a unified representation theorem for the Drazin inverse of linear operators in Hilbert space and a general error bound. Five specific expressions, computational procedures, and their error bounds for the Drazin inverse are uniformly derived from the unified representation theorem. 2002 Elsevier Science Inc. All rights reserved.

In this paper, we give a new additive formula for the Drazin inverse under conditions weaker than those used in some current literature on this subject. Also, we obtain representations for the Drazin inverse of a complex block matrix having generalized Schur complement equal to zero. 2000 Mathematics Subject Classification: 15A09

Block representations of the Drazin inverse of a bipartite matrix A = 2 4 0 B C 0 3 5 in terms of the Drazin inverse of the smaller order block product BC or CB are presented. Relationships between the index of A and the index of BC are determined, and examples are given to illustrate all such possible relationships.

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

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 matrix valued function and a result on diff...

In this paper we consider the Drazin inverse of a sum of two matrices and we derive additive formulas under conditions weaker than those used in some recent papers on the subject. Like a corollary we get the main results from the paper of H. Yang, X. Liu (The Drazin inverse of the sum of two matrices and its applications, Journ.Comp.Appl.Math., 235 (2011) 1412–1417). As an application we give s...

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 involving higher powers of the operators.

We give explicit representations of the generalized Drazin inverse of a block matrix having generalized Schur complement generalized Drazin invertible in Banach algebras. Also we give equivalent conditions under which the group inverse of a block matrix exists and a formula for its computation. The provided results extend earlier works given in the literature. 2010 Mathematics Subject Classific...

In this paper a representation is given for the Drazin inverse of a 2 × 2 operator matrix, extending to Banach spaces results of Hartwig, Li and Wei [SIAM J. Matrix Anal. Appl., 27 (2006) pp. 757–771]. Also, formulae are derived for the Drazin inverse of an operator matrix M under some new conditions.