几类广义Sylvester算子方程的可解性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1640-1652.

几类广义Sylvester算子方程的可解性

孙晓林,王华*()

^{内蒙古工业大学理学院数学系呼和浩特 010051}

收稿日期:2021-10-26 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 王华 E-mail:hrenly@163.com
基金资助:
国家自然科学基金(11961052);内蒙古自然科学基金(2022MS01005);内蒙古自然科学基金(2021LHMS01004);自治区直属高校基本科研业务费项目(JY220083);自治区直属高校基本科研业务费项目(JY20220151);内蒙古工业大学研究生教育教学改革项目(YJG2020027)

Solvability of Several Kinds of Ggeneralized Sylvester Operator Equations

Xiaolin Sun,Hua Wang*()

^{College of Sciences, Inner Mongolia University of Technology, Hohhot 010051}

Received:2021-10-26 Online:2022-12-26 Published:2022-12-16
Contact: Hua Wang E-mail:hrenly@163.com
Supported by:
the NSFC(11961052);the NSF of Inner Mongolia(2022MS01005);the NSF of Inner Mongolia(2021LHMS01004);the Basic Science Research Fund in the University Directly under the Inner Mongolia Autonomous Region(JY220083);the Basic Science Research Fund in the University Directly under the Inner Mongolia Autonomous Region(JY20220151);Tenching Reform of Postgraduate Education in Inner Mongolia University of Technology(YJG2020027)

摘要/Abstract

摘要：

该文讨论Hilbert空间上几类广义Sylvester算子方程和算子方程组的可解性.首先在正常算子的情况下, 给出两类算子方程AXB-XD=EB和AXB-CX=AE的解存在的充要条件; 其次利用算子对的一致等价性讨论三类算子方程的可解性; 最后给出当三角算子矩阵与对角算子矩阵相似时, 相应的算子方程组是可解的.

关键词: Sylvester方程, 算子方程, 正常算子, Putnam-Fuglede定理

Abstract:

In this paper, we discuss the solvability of some kinds of generalized Sylvester operator equations on Hilbert Spaces. Firstly, the necessary and sufficient conditions for the existence of solutions of AXB-XD=EB and AXB-CX = AE are given in the case of normal operators. Secondly, the solvability of three kinds of operator equations is discussed by using the uniform equivalence of operator pairs. Finally, when trigonometric operator matrix is similar to diagonal operator matrix, the corresponding operator equations are solvable.

Key words: Sylvester equation, Operator equation, Normal operator, Putnam-Fuglede's theorem

中图分类号:

O151.1

孙晓林,王华. 几类广义Sylvester算子方程的可解性[J]. 数学物理学报, 2022, 42(6): 1640-1652.

Xiaolin Sun,Hua Wang. Solvability of Several Kinds of Ggeneralized Sylvester Operator Equations[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1640-1652.

参考文献 9

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