On the solution of nonlinear operator equations and the invariant subspace

被引：0
作者：
Hua Wang
Jingsong Wu
Junjie Huang
机构：
[1] Inner Mongolia University of Technology,College of Sciences
[2] Inner Mongolia University,School of Mathematical Sciences
来源：
Advances in Operator Theory | 2023年 / 8卷
关键词：
Operator equation; Solution; Invariant subspace; 47A62; 47A15;
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摘要：
In this paper, we study nonzero solutions of the operator equation X2AX+XAX=BX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X^2AX+XAX=BX$$\end{document}, where A, B are given bounded linear operators on Hilbert spaces. Based on the invariant subspace of B, some necessary conditions and sufficient conditions are established for the existence of nonzero solutions of the equation. Moreover, we consider the infinitely many solutions and group invertible solutions. Finally, we give the connection between the nontrivial reducing subspace of B and the nonzero singular commuting solution of the equation.
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