The solution of the Yang-Baxter-like operator equation for rank-one operators

被引：0
|
作者：
Wang, Hua [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：
FILOMAT | 2024年 / 38卷 / 14期
关键词：
Yang-Baxter-like operator equation; rank-one operator; solution; MATRIX EQUATION; COMMUTING SOLUTIONS;
D O I：
10.2298/FIL2414817W
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let A is an element of B(H) be a rank-one operator, solutions of the Yang-Baxter-like operator equation AXA = XAX on Hilbert spaces are investigated. We derive necessary and sufficient conditions for an operator X is an element of B(H) being a solution of the equation. Further, a necessary and sufficient condition that the equation has a rank-one solution is obtained for an arbitrary operator A .
引用
收藏
页码：4817 / 4821
页数：5
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