Article contents
Stable perturbation in Banach algebras
Published online by Cambridge University Press: 09 April 2009
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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 2007
References
- 6
- Cited by