Additive results for the generalized Drazin inverse in a Banach algebra

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...

Generalized Drazin inverse of certain block matrices in Banach algebras

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.  

Representations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices

We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.

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...