Banach代数中上三角矩阵谱的填洞  

The Filling-in-holes of Spectra of Upper Triangular Matrices over Banach Algebras

作　　者：林丽琼[1] 

机构地区：[1]福州大学数学与计算机科学学院,福建福州350002

出　　处：《厦门大学学报（自然科学版）》2012年第2期153-156,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金项目(11171066);高等学校博士学科点专项科研基金项目(2010350311001)

摘　　要：设A是有单位元的Banach代数,给定a,b∈A,记2×2上三角矩阵Mc=(a c 0 b)∈M2(A),其中c∈A.证明了στ(a)∪στ(b)=στ(Mc)∪W,其中当στ=σ时,Wσ(a)∩σ(b)是σ(Mc)的某些洞的并;当στ=σl时,Wσr(a)∩(σl(b)\σl(a))包含在σl(a)的某些洞的并中,也包含在σl(Mc)的某些洞的并中;当στ=σr时,Wσl(b)∩(σr(a)\σr(b))包含在σr(b)的某些洞的并中,也包含在σr(Mc)的某些洞的并中.Let A be a Banach algebra with an identity.When a,b∈A are given,we denote by Mc a 2×2 upper triangular matrix of the form Mc=（a c0 b）∈M2（A）,where c∈A.We prove that στ（a）∪στ（b）=στ（Mc）∪W,where W is the union of certain of the holes in στ（Mc） which happen to be subsets of στ（a）∩στ（b） if στ=σ.If στ=σl,then Wσr（a）∩（σl（b）／σl（a）） is included in the union of certain of the holes in σl（a）,and it is also included in the union of certain of the holes in σl（Mc）.If στ=σr,then Wσl（b）∩（σr（a）／σr（b）） is included in the union of certain of the holes in σr（b）,and it is also included in the union of certain of the holes in σr（Mc）.

关 键 词：BANACH代数 上三角矩阵 谱 

分 类 号：O177.2[理学—数学]