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On the generalized Drazin inverse and generalized resolvent

Dragan S. DjordjevićStanimirović, Predrag S. — 2001

Czechoslovak Mathematical Journal

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 C * -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel....

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