Integral representations of the $g$-Drazin inverse in $C^*$-algebras

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.  

Integral representation of the Drazin inverse

Differentiability of the g-Drazin inverse

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...

Some Representations for the Generalized Drazin Inverse of Block Matrices in Banach Algebras

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...

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.