Banach代数中上三角矩阵的广义Drazin谱  

Generalized Drazin Spectrum of Upper Triangular Matrices in Banach Algebras

作　　者：庞永锋[1] 马栋 张丹莉 PANG Yongfeng;MA Dong;ZHANG Danli(Department of Mathematics,School of Science,Xi'an University of Architecture and Technology,Xi’an,Shaanxi,710055,P.R.China)

机构地区：[1]西安建筑科技大学理学院数学系,西安陕西710055

出　　处：《数学进展》2021年第3期429-436,共8页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11401757);陕西省自然科学基金(No.2019JM252);西安建筑科技大学基础研究基金(No.JC0621)。

摘　　要：设A是含单位元e的Banach代数,a,b,c∈A,M_(c)=(a c o b)∈M_(2)(A).本文提出了 Banach代数中元素的左、右广义Drazin可逆的概念.定义集合σgD(a)={λ∈C:a - λe不是广义Drazin可逆的}为元素a的广义Drazin谱.证明了σgD(a)∪σgD(a)=σgD(M_(c))∪W_(g),其中 W_(g) 是σgD (M_(c))的某些洞且W_(g)■σgD(a)∩σgD(b),或者更精细地W_(g)■σrgD(a)∩σlgD(b).此外,还研究了 Banach代数中元素的广义Drazin谱的其他性质.Let A be a Banach algebra with unit e and a,b,c∈A,M_(c)=(a c o b)∈M_(2)(A).The concepts of left and right generalized Drazin invertible of elements in a Banach algebra are proposed.A generalized Drazin spectrum of a is defined by σgD(a)={λ∈C:a-λe is not generalized Drazin invertible}.It is shown thatσgD(a)∪σgD(b)=σgD(Mc)∪W_(g),where W_(g) is a union of certain holes in σgD(M_(c)) and W_(g)■σgD(a)∩σgD(b),or more finely W_(g)■σrgD(a)∩σlgD(b).In addition,some properties of generalized Drazin spectrum of elements in a Banach algebra are studied.

关 键 词：BANACH代数 广义Drazin逆 广义Drazin谱 上三角矩阵 

分 类 号：O177.2[理学—数学]