@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 {6553,
	title = {Generalized derivation, SVEP, finite ascent, range closure},
	journal = {Filomat},
	volume = {34},
	number = {10},
	year = {2020},
	pages = {3473-3482},
	author = {Farida Lombarkia and Megri, Sabra}
}
@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}
}
@article {5256,
	title = {Asymmetric Fuglede Putnam\&$\#$39;s Theorem for operators reduced by their eigenspaces},
	journal = {FILOMAT},
	year = {2017},
	abstract = {
	Fuglede-Putnam Theorem have been proved for a considerably large number of class of operators. In this paper by using the spectral theory, we obtain a theoretical and general framework from which Fuglede-Putnam theorem may be promptly established for many classes of operators.

},
	author = {Farida Lombarkia and Mohamed Amouch}
}
@article {6566,
	title = {Asymmetric Fuglede Putnam{\textquoteright}s Theorem for operators reduced by their eigenspaces},
	journal = {arXiv preprint arXiv:1603.07494},
	year = {2016},
	author = {Farida Lombarkia and Mohamed Amouch}
}
