@article {6569,
	title = {Selfadjoint operators, normal operators, and characterizations},
	journal = {Operators and Matrices},
	volume = {13},
	year = {2019},
	pages = {835-842},
	author = {AMEUR SEDDIK}
}
@article {6574,
	title = {SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A1XA},
	year = {2019},
	author = {Warda Merahi and Said Guedjiba}
}
@article {5266,
	title = {SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A1XA*1= B1 AND A2XA\&lowast;2 = B2},
	journal = {MATEMATICKI VESNIK ˇ MATEMATIQKI VESNIK},
	volume = {71},
	number = {3},
	year = {2019},
	pages = {214{\textendash}229},
	author = {Warda Merahi and Said Guedjiba}
}
@article {5259,
	title = {On Numerical Radius Inequalities for Operator Matrices},
	journal = {Numerical Functional Analysis and Optimization},
	volume = {40},
	number = {11},
	year = {2019},
	pages = {1231-1241},
	author = {Hanane Guelfen and Fuad Kittaneh}
}
@article {5258,
	title = {SELFADJOINT OPERATORS, NORMAL OPERATORS, AND CHARACTERIZATIONS},
	journal = {Operators and Matrices},
	volume = {13},
	number = {3},
	year = {2019},
	pages = {835{\textendash}842},
	abstract = {
	Let B(H) be the C* -algebra of all bounded linear operators acting on a complex separable Hilbert space H . We shall show that:



	1. The class of all selfadjoint operators in B(H) multiplied by scalars is characterized by ∀X ∈ B(H), S2X +XS2\&nbsp;=\&gt;2||SXS||, (S ∈ B(H)).



	2. The class of all normal operators in B(H) is characterized by each of the three following properties (where DS = S*S-SS* , for S ∈ B(H)),



	(i) ∀X ∈ B(H), S2X + XS2\&nbsp;=\&gt;2||SXS||,(S ∈ B(H)),



	(ii) S*DSS = 0 = SDSS*,(S ∈ B(H)),



	(iii) S*DSS=\&gt; 0 =\&gt;SDSS*,(S ∈ B(H)).



	\&nbsp;

},
	author = {Seddik Ameur}
}
@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}
}
