Research ArticleNo Access

Left and right-Drazin inverses in rings and operator algebras

Yanxun Ren

Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. China

E-mail Address: renyanxun@tjufe.edu.cn

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and

Lining Jiang

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China

E-mail Address: jianglining@bit.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0219498824500646Cited by:3 (Source: Crossref)

Abstract

The paper introduces the left and right versions of the large class of Drazin inverses in terms of the left and right annihilators in a ring, which are called left-Drazin and right-Drazin inverses. We characterize some basic properties of these one-sided Drazin inverses, and discuss Jacobson’s lemma for them. In addition, the relation between the Drazin inverses and these two one-sided inverses is given by means of the spectrum and the operator decomposition. As an application, the left-Drazin and right-Drazin invertibilities in the Calkin algebra are investigated.

Communicated by P. Ara

Keywords:

AMSC: 16U90, 47A53

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