Banach代数中两个元素之和与积的广义Drazin逆

吉林大学学报(理学版) ›› 2023, Vol. 61 ›› Issue (3): 547-552.

Banach代数中两个元素之和与积的广义Drazin逆

郭丽, 胡广丽, 王安琪, 栾天

北华大学数学与统计学院, 吉林吉林 132013

收稿日期:2022-11-18 出版日期:2023-05-26 发布日期:2023-05-26
通讯作者: 栾天 E-mail:luantian@163.com

Generalized Drazin Inverse of Sum and Product of Two Elements in Banach Algebra

GUO Li, HU Guangli, WANG Anqi, LUAN Tian

School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China

Received:2022-11-18 Online:2023-05-26 Published:2023-05-26

摘要/Abstract

摘要： 令a,b为具有单位元1的Banach代数A中两个广义Drazin逆的元素, a^d为a的广义Drazin逆. 利用Banach代数中的幂等系统考虑两个元素之和与积的广义Drazin逆, 在ab²=bab, b^πba²=b^πaba, a^db²=ba^db等条件下给出a,b之和与积的广义Drazin逆的表达式.

关键词: 广义Drazin逆, 拟幂零元, Banach代数

Abstract: Let a,b be two generalized Drazin invertible elements in a Banach algebra A with unity 1, a^d be the generalized Drazin inverse of a. The generalized Drazin inverse of the sum and product of two elements in a Banach algebra was considered by means of the system of idempotents. The expressions for the generalized Drazin inverse of the sum and product of a and b were given under some conditions such as ab²=bab, b^πba²=b^πaba, a^db²=ba^db etc.

Key words: generalized Drazin inverse, quasi-nilpotent element, Banach algebra

中图分类号:

郭丽, 胡广丽, 王安琪, 栾天. Banach代数中两个元素之和与积的广义Drazin逆[J]. 吉林大学学报(理学版), 2023, 61(3): 547-552.

GUO Li, HU Guangli, WANG Anqi, LUAN Tian. Generalized Drazin Inverse of Sum and Product of Two Elements in Banach Algebra[J]. Journal of Jilin University Science Edition, 2023, 61(3): 547-552.

[1]	郭丽, 许小杰, 谷天瑜, 于德跃, 雷鸣. Banach代数中广义Drazin逆的相关结果[J]. 吉林大学学报(理学版), 2020, 58(3): 595-598.
[2]	郭丽, 丁许一. Banach代数中两个元素之和广义Drazin逆的表示[J]. 吉林大学学报(理学版), 2017, 55(06): 1465-1468.