On the solution of nonlinear operator equations and the invariant subspace

被引：0

作者：

Wang, Hua ^{[1
]}

Wu, Jingsong ^{[1
]}

Huang, Junjie ^{[2
]}

机构：

[1] Inner Mongolia Univ Technol, Coll Sci, Hohhot 010051, Peoples R China

[2] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

来源：

ADVANCES IN OPERATOR THEORY | 2023年 / 8卷 / 04期

关键词：

Operator equation; Solution; Invariant subspace; MATRIX;

D O I：

10.1007/s43036-023-00291-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study nonzero solutions of the operator equation X-2 AX + XAX = BX, 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.

引用

页数：10

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