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
收藏
页数：16
相关论文
共 50 条
  • [31] RIGHT INVERSES IN D-R ALGEBRAS WITH UNIT
    PRZEWORSKAROLEWICZ, D
    VONTROTHA, H
    JOURNAL OF INTEGRAL EQUATIONS, 1981, 3 (03): : 245 - 259
  • [32] Left and right resolvents and new characterizations of left and right generalized Drazin invertible operators
    Ounadjela, Djalal
    Messirdi, Bekkai
    Messirdi, Sofiane
    FILOMAT, 2023, 37 (01) : 21 - 36
  • [33] Left w-Core Inverses in Rings with Involution
    Zhu, Huihui
    Wang, Chengcheng
    Wang, Qing-Wen
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (06)
  • [34] On the Weighted Pseudo Drazin Invertible Elements in Associative Rings and Banach Algebras
    Chen, Jianlong
    Chen, Xiaofeng
    Zguitti, Hassane
    FILOMAT, 2019, 33 (19) : 6359 - 6367
  • [35] Left w-Core Inverses in Rings with Involution
    Huihui Zhu
    Chengcheng Wang
    Qing-Wen Wang
    Mediterranean Journal of Mathematics, 2023, 20
  • [36] Left and right G-outer inverses
    Mosic, Dijana
    Wang, Long
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (17): : 3319 - 3344
  • [37] The p-Drazin Inverse for Operator Matrix over Banach Algebras
    Chen, Huanyin
    Zou, Honglin
    Calci, Tugce Pekacar
    Kose, Handan
    FILOMAT, 2020, 34 (14) : 4597 - 4605
  • [38] Nonlinear Lie Centralizers on Rings and Operator Algebras
    Zhang, Fangjuan
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2014, 52 (04): : 107 - 116
  • [39] Some Drazin invertible elements in Banach algebras and applications to operator equations solutions
    Belhadi, Ahfouda
    Mansour, Abdelouahab
    Salmi, Abdelouahab
    Italian Journal of Pure and Applied Mathematics, 2019, (42): : 428 - 435
  • [40] Left and right distributive rings
    Tuganbaev, AA
    MATHEMATICAL NOTES, 1995, 58 (3-4) : 1100 - 1116
12345