Perturbation Bound of the Group Inverse and the Generalized Schur Complement in Banach Algebra

Abstract

We investigate the relative perturbation bound of the group inverse and also consider the perturbation bound of the generalized Schur complement in a Banach algebra.

Perturbation for group inverse in a Banach algebra

“…Liu et al investigated the perturbation of group inverse under the conditions a d baa d < 1, a π ba = 0 (see [6,Theorem 2.8]). They further studied the group invertibility under the condition a d baa d < 1, a π ba = aba π (see [6,Theorem 2.12]). These inspire us to explore the perturbation for group invertibility in a more general setting.…”