Stable perturbation in Banach algebras
Yifeng Xue · Journal of the Australian Mathematical Society · 2007
Abstract Let be a unital Banach algebra. Assume that a has a generalized inverse a + . Then is said to be a stable perturbation of a if . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation is closely related to the gap function . These results will be applied to error estimates for perturbations of the Moore-Penrose inverse in C*–algebras and the Drazin inverse in Banach algebras.