数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1143-1150.doi: 10.1016/S0252-9602(18)30804-X

• 论文 • 上一篇    下一篇

SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA

张肖, 吉国兴   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China
  • 收稿日期:2017-08-09 修回日期:2018-01-23 出版日期:2018-08-25 发布日期:2018-08-25
  • 通讯作者: Guoxing JI,E-mail:gxji@snnu.edu.cn E-mail:gxji@snnu.edu.cn
  • 作者简介:Xiao ZHANG,E-mail:1964263480@qq.com
  • 基金资助:

    This research is supported by the National Natural Science Foundation of China (11371233).

SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA

Xiao ZHANG, Guoxing JI   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China
  • Received:2017-08-09 Revised:2018-01-23 Online:2018-08-25 Published:2018-08-25
  • Contact: Guoxing JI,E-mail:gxji@snnu.edu.cn E-mail:gxji@snnu.edu.cn
  • Supported by:

    This research is supported by the National Natural Science Foundation of China (11371233).

摘要:

In this paper, we present some necessary and sufficient conditions for the existence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB=C=BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.

关键词: operator equation, Moore-Penrose inverse, solution, hermitian solution, positive solution

Abstract:

In this paper, we present some necessary and sufficient conditions for the existence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB=C=BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.

Key words: operator equation, Moore-Penrose inverse, solution, hermitian solution, positive solution