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Stable perturbation in Banach algebras

Published online by Cambridge University Press:  09 April 2009

Yifeng Xue
Affiliation:
Department of MathematicsEast China Normal UniversityShanghai [email protected], [email protected].
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

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