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2012•Abstract and Applied AnalysisOpen access

On Stable Perturbations of the Generalized Drazin Inverses of Closed Linear Operators in Banach Spaces

Qianglian Huang, Lanping Zhu, Xiaoru Chen, Chang Zhang

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Abstract

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

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What this paper is about

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

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Available abstract

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

Key concepts: Mathematics, Drazin inverse, Linear operators, Banach space, Pure mathematics, Perturbation (astronomy), Mathematical analysis, Inverse

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