@article {6555,
	title = {HERIMITIAN SOLUTIONS TO THE EQUATION AXA+ BY B= C, FOR HILBERT SPACE OPERATORS},
	year = {2021},
	author = {Amina Boussaid and Farida Lombarkia}
}
@article {5254,
	title = {Operator equations and inner inverses of elementary operators},
	journal = { Linear and Multilinear Algebra },
	year = {2019},
	abstract = {
	Let\&nbsp;E,F,G,D\&nbsp;be infinite complex Banach spaces and\&nbsp;B(F,E)\&nbsp;the Banach space of all bounded linear operators from\&nbsp;F\&nbsp;into\&nbsp;E. Consider\&nbsp;A1,A2∈B(F,E),\&nbsp;B1,B2∈B(D,G)B1,B2∈B(D,G). Let\&nbsp;MA1,B1:X{\textrightarrow}A1XB1\&nbsp;be the multiplication operator on\&nbsp;B(G,F)\&nbsp;induced by\&nbsp;A1,B1. In particular,\&nbsp;LA1=MA1,I\&nbsp;and\&nbsp;RB1=MI,B1, where\&nbsp;I\&nbsp;is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on\&nbsp;B(G,F)B(G,F)\&nbsp;is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations\&nbsp;MA1,B1(X)=C1 and\&nbsp;MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation\&nbsp;MA,B(X)=C. As a consequence, we obtain well-known results of Dajic{\textasciiacute}\&nbsp;and Koliha.

},
	author = {Farida Lombarkia and Amina Boussaid}
}
