一类非线性算子方程的解
Solutions to a Class of Nonlinear Operator Equations
刘畅 1王华1
作者信息
- 1. 内蒙古工业大学理学院,呼和浩特 010051
- 折叠
摘要
在Hilbert空间中讨论算子方程X2AX+XAX=BX解的相关问题.首先,利用算子的特征值分别给出B=2A时算子方程存在秩一解以及秩一幂等交换解的充分条件.进一步,在算子具有特征矩阵时给出算子方程存在有限秩解以及可交换的有限秩解的充要条件.其次,在一定条件下给出算子方程可解的必要条件和充分条件.
Abstract
The problems related to the solution of operator equation X2AX+XAX=BX in Hilbert space are discussed.Firstly,the sufficient conditions for the existence of rank-one solutions and rank-one idempotent commutative solutions of the operator equations at B=2A are given by using the eigenvalues of the operators.Furthermore,the necessary and sufficient conditions for the existence of finite rank solutions and commutative finite rank solutions of operator equations are given when operators have eigenmatrices.Sec-ondly,the necessary and sufficient conditions for the solvability of the operator equation are given under certain conditions.
关键词
算子方程/有限秩算子/不变子空间Key words
Operator equation/Finite rank operator/Invariant subspace引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据