@article{Zhang2023, 
author = {Haiyan Zhang and Yanni Dou and Weiyan Yu},
title = {Real positive solutions of operator equations    A  X  =  C and    X  B  =  D},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {15214-15231},
keywords = {reduced solution, real positive solution, operator equation},
url = {https://www.sciopen.com/article/10.3934/math.2023777},
doi = {10.3934/math.2023777},
abstract = {In this paper, we mainly consider operator equations    A  X  =  C and    X  B  =  D in the framework of Hilbert space. A new representation of the reduced solution of    A  X  =  C is given by a convergent operator sequence. The common solutions and common real positive solutions of the system of two operator equations    A  X  =  C and    X  B  =  D are studied. The detailed representations of these solutions are provided which extend the classical closed range case with a short proof.}
}