On the generalized Drazin inverse and generalized resolvent
Dragan S. Djordjević, Stanimirović, Predrag S. (2001)
Czechoslovak Mathematical Journal
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We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range...