Schur’s theorem and the Drazin inverse

Continuity of the Drazin Inverse

In this paper we investigate the continuity of the Drazin inverse of a bounded linear operator on Banach space. Then as a corollary, among other things, we get the well known result of Campbell and Meyer ([1]) for the continuity of the Drazin inverse of square matrix.

Ela Perturbation of the Generalized Drazin Inverse

In this paper, we investigate the perturbation of the generalized Drazin invertible matrices and derive explicit generalized Drazin inverse expressions for the perturbations under certain restrictions on the perturbing matrices.

Cline’s formula for the generalized Drazin inverse

†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This for...

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...