Left and right-Drazin inverses in rings and operator algebras

被引：3
|
作者：
Ren, Yanxun [1 ]
Jiang, Lining [2 ]
机构：
[1] Tianjin Univ Finance & Econ, Dept Math, Tianjin 300222, Peoples R China
[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2024年 / 23卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Left-Drazin and right-Drazin inverses; Jacobson's lemma; Fredholm operators; JACOBSONS LEMMA; INVERTIBILITY; RESOLVENT; ELEMENTS; THEOREM; POLES;
D O I：
10.1142/S0219498824500646
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：16
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