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

共 50 条

[1] On the solution of nonlinear operator equations and the invariant subspace
Hua Wang
Jingsong Wu
Junjie Huang
Advances in Operator Theory, 2023, 8
[2] On approximate solution of nonlinear operator equations
Tanana, VP
SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (05) : 1017 - 1025
[3] On approximate solution of nonlinear operator equations
V. P. Tanana
Siberian Mathematical Journal, 1998, 39 : 1017 - 1025
[4] ON EXTENSION AND SOLUTION OF NONLINEAR OPERATOR EQUATIONS
PETRYSHYN, WV
ILLINOIS JOURNAL OF MATHEMATICS, 1966, 10 (02) : 255 - +
[5] ON THE SUBSPACE CHOICE IN PROJECTION METHODS OF THE SOLUTION OF OPERATOR-EQUATIONS
KOLIADIN, VL
KRAVCHENKO, VF
DOKLADY AKADEMII NAUK SSSR, 1987, 296 (05): : 1050 - 1052
[6] On some restrictions of an operator to an invariant subspace
Wojcik, Pawel
LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 450 : 1 - 6
[7] SOLUTION OF NONLINEAR OPERATOR EQUATIONS WITH CRITICAL POINTS
DAVIS, J
SIAM REVIEW, 1966, 8 (04) : 562 - &
[8] APPROXIMATE SOLUTION OF SOME NONLINEAR OPERATOR EQUATIONS
LAVRENTE.MM
ANIKONOV, YE
FAZYLOV, FN
DOKLADY AKADEMII NAUK SSSR, 1971, 200 (04): : 770 - &
[9] A SOLUTION TO THE INVARIANT SUBSPACE PROBLEM
READ, CJ
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1984, 16 (JUL) : 337 - 401
[10] Preconditioned Subspace Descent Methods for the Solution of Nonlinear Systems of Equations
Kaporin, Igor
OPTIMIZATION AND APPLICATIONS, OPTIMA 2019, 2020, 1145 : 164 - 179

← 1 2 3 4 5 →