应用泛函分析学报
應用汎函分析學報
응용범함분석학보
ACTA ANALYSIS FUNCTIONALIS APPLICATA
2003年
1期
9-12
,共4页
算子方程%不变子空间%约化子空间%正规算子
算子方程%不變子空間%約化子空間%正規算子
산자방정%불변자공간%약화자공간%정규산자
operator equations%invariant subspaces%reducing subspaces%normal operators
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AX=XZ=XAX的解的充分必要条件.
用A的不變子空間作參數,給齣瞭算子方程AX=XAX的全部解. 噹A是單射或稠值域時,或者噹A是正規算子時,給齣瞭算子方程AX=XA=XAX的全部解. 我們還給齣正規算子X是算子方程AX=XZ=XAX的解的充分必要條件.
용A적불변자공간작삼수,급출료산자방정AX=XAX적전부해. 당A시단사혹주치역시,혹자당A시정규산자시,급출료산자방정AX=XA=XAX적전부해. 아문환급출정규산자X시산자방정AX=XZ=XAX적해적충분필요조건.
In this paper, we give the representation of the solution set of the operator equation AX=XAX in terms of the invariant subspaces of A and the representation of solution set of AX=XA=XAX in the cases that A is a normal operator or an operator with dense range or with injectivity. We also give a sufficient and necessary condition for a normal operator X to be a solution of equation XAX=XA=XA.
