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.

引用

页数：16

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