算子方程AX=XAX的解  

Solutions to the operator equation AX=XAX

作　　者：许俊莲[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2010年第3期6-8,共3页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：宝鸡文理学院科研基金资助项目(Zk08107)

摘　　要：目的讨论算子方程AX=XAX存在非平凡解(即X≠0,I)的充要条件,其中A是作用在Hilbert空间H上的有界线性算子。方法利用算子分块的技巧。结果与结论得出了算子方程AX=XAX存在非平凡解(即X≠0,I)的充要条件是算子A在H中存在非平凡的不变子空间,并给出新的证明。Aim To discuss the necessary and sufficient conditions for the existence of nontrivial solutions（that is X≠0,I） to the operator equation AX=XAX are discussed among which A is a bounded linear operator on a Hilbert space H.Methods The technique of block operator matrix is used to discuss the problem.Results and Conclusion The necessary and sufficient condition for the existence of nontrivial solutions（that is X≠0,I） to the operator equation AX=XAX is the operator A has nontrivial invariant subspaces in H.In addition,the new proof is given.

关 键 词：算子方程 不变子空间 非平凡解 

分 类 号：O177.1[理学—数学]