几类广义Sylvester算子方程的可解性  

Solvability of Several Kinds of Ggeneralized Sylvester Operator Equations

作　　者：孙晓林 王华[1] Sun Xiaolin;Wang Hua(College of Sciences,Inner Mongolia University of Technology,Hohhot 010051)

机构地区：[1]内蒙古工业大学理学院数学系,呼和浩特010051

出　　处：《数学物理学报（A辑）》2022年第6期1640-1652,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11961052);内蒙古自然科学基金(2022MS01005,2021LHMS01004);自治区直属高校基本科研业务费项目(JY220083,JY20220151);内蒙古工业大学研究生教育教学改革项目(YJG2020027)。

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.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.

关 键 词：SYLVESTER方程 算子方程 正常算子 Putnam-Fuglede定理 

分 类 号：O151.1[理学—数学] O177.1[理学—基础数学]