Geodesic
On the generalized Drazin inverse and generalized resolvent
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 617-634 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $C^*$-algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel. Also, $2\times 2$ operator matrices are considered. As corollaries, we get some well-known results.
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. Also, $2\times 2$ operator matrices are considered. As corollaries, we get some well-known results.
Classification : 46H30, 46L05, 47A05, 47A10
Keywords: Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices 
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Djordjević, Dragan S.; Stanimirović, Predrag S. On the generalized Drazin inverse and generalized resolvent. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 617-634. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a12/

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