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

doi:10.1016/S0252-9602(18)30804-X

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (4): 1143-1150.doi: 10.1016/S0252-9602(18)30804-X

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

Xiao ZHANG, Guoxing JI

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).

Abstract

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

Xiao ZHANG, Guoxing JI. SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA[J].Acta mathematica scientia,Series B, 2018, 38(4): 1143-1150.

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References 15

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

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