1. On the generalized Drazin inverse and generalized resolvent
- Creator:
- Djordjević, Dragan S. and Stanimirović, Predrag S.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Drazin inverse, generalized resolvent, limit processes, outer inverses, and operator matrices
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public