Expressions for the g-Drazin inverse in a Banach algebra

Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra

We present some new representations for the generalized Drazin inverse of a block matrix with generalized Schur complement being generalized Drazin invertible in a Banach algebra under conditions weaker than those used in recent papers on the subject.

Ela Some Additive Results for the Generalized Drazin Inverse in a Banach Algebra

In this note, additive results are presented for the generalized Drazin inverse in Banach algebra. Necessary and sufficient conditions are given for the generalized Drazin invertibility of the sum of two commuting generalized Drazin invertible elements. These results are a generalization of the results from the paper [C.Y. Deng and Y. Wei. New additive results for the generalized Drazin inverse...

Some additive results for the generalized Drazin inverse in a Banach algebra

Representations for the Generalized Drazin Inverse in a Banach Algebra (communicated by Fuad Kittaneh)

The Drazin inverse has important applications in matrix theory and fields such as statistics, probability, linear systems theory, differential and difference equations, Markov chains, and control theory ([1, 2, 11]). In [9], Koliha extended the Drazin invertibility in the setting of Banach algebras with applications to bounded linear operators on a Banach space. In this paper, Koliha was able t...

Group Inverse and Generalized Drazin Inverse of Block Matrices in a Banach Algebra

Let A be a complex unital Banach algebra with unit 1. The sets of all invertible and quasinilpotent elements (σ(a) = {0}) of A will be denoted by A and A, respectively. The group inverse of a ∈ A is the unique element a ∈ A which satisfies aaa = a, aaa = a, aa = aa. If the group inverse of a exists, a is group invertible. Denote by A the set of all group invertible elements of A. The generalize...