关于算子方程AX=XAX与AX=XA=XAX(英文)  

On the Operator equations AX=XAX and AX=XA=XAX

作　　者：安桂梅[1] 白朝芳[1] 杜拴平[1] 

机构地区：[1]山西师范大学数学与计算机系,山西临汾041004

出　　处：《应用泛函分析学报》2003年第1期9-12,共4页Acta Analysis Functionalis Applicata

基　　金：NNSF of China;the NSF of Shanxi Province and the Youth Scientific and TechnologicalFoundation of Shanxi Province

摘　　要：用 A的不变子空间作参数 ,给出了算子方程 AX=XAX的全部解 .当 A是单射或稠值域时 ,或者当 A是正规算子时 ,给出了算子方程 AX=XA=XAX的全部解 .我们还给出正规算子 X是算子方程in this paper, we give the representation of th E solution set of the operator equation ax=xax in terms of the invariant subs Paces of a and the representation of solution set of ax=xa=xax i N the cases that a is a normal operator or an operator with dense range or w Ith injectivity. We also give a sufficient and necessary condition for a normal Operator x to be a solution of equation xax=xa=xa.=

关 键 词：不变子空间 正规算子 HILBERT空间 级化子空间 算子方程 

分 类 号：O177.1[理学—数学]