On the generalized Drazin inverse and generalized resolvent

Title:

On the generalized Drazin inverse and generalized resolvent

Creator:

Djordjević, Dragan S. and Stanimirović, Predrag S.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:80094fd8-665e-4b85-87c4-30b0448a6ac7
uuid:80094fd8-665e-4b85-87c4-30b0448a6ac7

Subject:

Drazin inverse, generalized resolvent, limit processes, outer inverses, and operator matrices

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

617-634

Source:

Czechoslovak Mathematical Journal | 2001 Volume:51 | Number:3

Harvested from:

CDK

Metadata only:

false