On the Generalized Drazin Inverse and Generalized Resolvent

被引：0
作者：
Dragan S. Djordjevic
Predrag S. Stanimirovic
机构：
[1] University of Nis,Faculty of Sciences, Department of Mathematics
来源：
Czechoslovak Mathematical Journal | 2001年 / 51卷
关键词：
Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices;
D O I：
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学科分类号：
摘要：
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 × 2 operator matrices are considered. As corollaries, we get some well-known results.
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页码：617 / 634
页数：17
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