Banach代数中元素乘积的广义Drazin可逆性  

Generalized Drazin invertibility of the product of elements in Banach algebras

作　　者：邹红林 曾月迪 陈建龙[1] Zou Honglin;Zeng Yuedi;Chen Jianlong(School of Mathematics,Southeast University,Nanjing 210096,China;College of Basic Science,Zhejiang Shuren University,Hangzhou 310015,China;School of Mathematics and Finance,Putian University,Putian 351100,China;Key Laboratory of Applied Mathematics(Putian University),Fujian Province University,Putian 351100,China)

机构地区：[1]东南大学数学学院,南京210096 [2]浙江树人学院基础学院,杭州310015 [3]莆田学院数学与金融学院,莆田351100 [4]应用数学福建省高校重点实验室(莆田学院),莆田351100

出　　处：《东南大学学报（自然科学版）》2023年第1期182-186,共5页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(12171083);福建省自然科学基金资助项目(2020J01908);中国博士后科学基金资助项目(2020M671281);应用数学福建省高校重点实验室(莆田学院)开放课题资助项目(SX202202)。

摘　　要：在广义交换条件下,研究了Banach代数中元素乘积的广义Drazin逆的存在性和表达式问题.设a,b是Banach代数中2个广义Drazin可逆元.若a^(3)b=a^(2)ba,a^(2)b^(2)=(ab)^(2)=ab^(2)a,且bab^(2)=b^(2)ab,则ab是广义Drazin可逆元,且(ab)d=adbd.若a^(3)b=a^(2)ba,ba^(2)b=(ba)^(2),ab^(2)a=(ab)^(2),且b^(3)a=b^(2)ab,则ab是广义Drazin可逆元,且(ab)d=abd(ad)^(2).所得结果推广和改进了一些文献中的相关结论,并被应用到元素乘积的群逆上.Under the generalized commuting conditions, the problems on the existence and the expression of the generalized Drazin inverse of the product of the elements are studied in Banach algebras. Let a,b be two generalized Drazin invertible elements in a Banach algebra. If a^(3)b=a^(2)ba, a^(2)b^(2)=(ab)^(2)=ab^(2)a and bab^(2)=b^(2)ab, then ab is generalized Drazin invertible with(ab)d=adbd. If a^(3)b=a^(2)ba, ba^(2)b=(ba)^(2), ab^(2)a=(ab)^(2) and b^(3)a=b^(2)ab, then ab is generalized Drazin invertible and(ab)d=abd(ad)^(2). The results obtained extend and improve the relevant conclusions in some literature. Meanwhile, they are applied to the group inverse.

关 键 词：广义Drazin逆 BANACH代数 交换性 

分 类 号：O151.2[理学—数学]