Banach代数中两个元素之和与积的广义Drazin逆  

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

作　　者：郭丽[1] 胡广丽 王安琪 栾天[1] GUO Li;HU Guangli;WANG Anqi;LUAN Tian(School of Mathematics and Statistics,Beihua University,Jilin 132013,Jilin Province,China)

机构地区：[1]北华大学数学与统计学院,吉林吉林132013

出　　处：《吉林大学学报（理学版）》2023年第3期547-552,共6页Journal of Jilin University:Science Edition

基　　金：吉林省科技发展计划项目(批准号:YDZJ202201ZYTS648);吉林省教育厅科学技术研究规划项目(批准号:JJKH20210028KJ,2014213);北华大学研究生创新项目(批准号:2022[002],2022[031]).

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ab 2=bab,b^(π)ba^(2)=bπaba,a^(d)b 2=ba^(d)b等条件下给出a,b之和与积的广义Drazin逆的表达式.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 ab 2=bab,b^(π)ba^(2)=bπaba,a^(d)b 2=ba^(d)b etc.

关 键 词：广义Drazin逆 拟幂零元 BANACH代数 

分 类 号：O151.21[理学—数学]