Banach代数中广义Drazin逆的相关结果

吉林大学学报(理学版) ›› 2020, Vol. 58 ›› Issue (3): 595-598.

Banach代数中广义Drazin逆的相关结果

郭丽, 许小杰, 谷天瑜, 于德跃, 雷鸣

北华大学数学与统计学院, 吉林吉林 132013

收稿日期:2019-08-23 出版日期:2020-05-26 发布日期:2020-05-20
通讯作者: 雷鸣 E-mail:bhdxlm@163.com

Relevant Results on Generalized DrazinInverses in a Banach Algebra

GUO Li, XU Xiaojie, GU Tianyu, YU Deyue, LEI Ming

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

Received:2019-08-23 Online:2020-05-26 Published:2020-05-20
Contact: LEI Ming E-mail:bhdxlm@163.com

摘要/Abstract

摘要： 令a,b均为Banach代数中广义Drazin可逆的元素, a^d为a的广义Drazin逆, a^π=1-aa^d. 用Banach代数中的幂等元给出元素a,b在ab^π=a, b^πba^π=b^πb, b^πa^πa²b=b^πa^πaba, b^πa^πb²a=b^πa^πbab等条件下a+b广义Drazin逆的表达式.

关键词: 广义Drazin逆, Banach代数, 拟幂零元

Abstract: Let a,b be two generalized Drazin invertible elements in a Banach algebra, a^d be the generalized Drazin inverse of aaⁿd a^π=1-aa^d. We gave the expressions for the generalized Drazin [JP2]inverse of the sum a+b under some conditions such as ab^π=a, b^πba^π=b^πb, b^πa^πa²b=b^πa^πaba, b^πa^πb²a=b^πa^πbab etc by using the idempotent element in a Banach algebra.

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

中图分类号:

O151.21

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.

GUO Li, XU Xiaojie, GU Tianyu, YU Deyue, LEI Ming. Relevant Results on Generalized DrazinInverses in a Banach Algebra[J]. Journal of Jilin University Science Edition, 2020, 58(3): 595-598.