<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amina Boussaid</style></author><author><style face="normal" font="default" size="100%">Farida Lombarkia</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HERIMITIAN SOLUTIONS TO THE EQUATION AXA+ BY B= C, FOR HILBERT SPACE OPERATORS</style></title><secondary-title><style face="normal" font="default" size="100%">University of Niš publishes Facta Universitatis journal</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2021</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://casopisi.junis.ni.ac.rs/index.php/FUMathInf/article/view/5843</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">36</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	Let A, A_{1},&amp;nbsp; A_{2}, B, B_{1}, B_{2}, C_{1} and C_{2} be linear bounded operators on Hilbert spaces. In this paper, by using generalized inverses, we establish necessary and sufficient conditions for the existence of a common solution and give the form of the general common solution of the operator equations A_{1}XB_{1}=C_{1} and A_{2}XB_{2}=C_{2}, we apply this result to determine new necessary and sufficient conditions for the existence of Hermitian solutions&amp;nbsp; and give the form of the general Hermitian solution to the operator equation AXB=C. As a consequence, we give necessary and sufficient condition for the existence of Hermitian solution to the operator equation AXA^{*}+BYB^{*}=C.
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