@article {62684,
	title = {HERIMITIAN SOLUTIONS TO THE EQUATION AXA+ BY B= C, FOR HILBERT SPACE OPERATORS},
	journal = {University of Ni{\v s} publishes Facta Universitatis journal},
	volume = {36},
	number = {1},
	year = {2021},
	month = {2021},
	abstract = {
	Let A, A_{1},\&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\&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.

},
	url = {http://casopisi.junis.ni.ac.rs/index.php/FUMathInf/article/view/5843},
	author = {Amina Boussaid and Farida Lombarkia}
}
