Resumen de Stable perturbation in Banach algebras

Yifeng Xu

• Let be a unital Banach algebra. Assume that a has a generalized inverse a+. Then a=a+a is said to be a stable perturbation of a if a(1-aa+)=0 . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation a(1-aa+)=0 is closely related to the gap function (aa). 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.