Stable perturbation in Banach algebras

• Autores: Yifeng Xu
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 83, Nº 2, 2007, págs. 271-284
• Idioma: inglés
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• Resumen

  • 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.