@article {63572,
	title = {SELFADJOINT OPERATORS, NORMAL OPERATORS, AND CHARACTERIZATIONS},
	journal = {Operators and MatricesOperators and Matrices},
	volume = {13},
	year = {2019},
	month = {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 = {Ameur, Seddik}
}
@article {65030,
	title = {On the characterizations of some distinguished subclasses of Hilbert space operators},
	journal = {Acta Scientiarum MathematicarumActa Scientiarum Mathematicarum},
	volume = {84},
	year = {2018},
	month = {2018},
	pages = {611-627},
	abstract = {In this note, we present several characterizations for some distinguished classes of bounded Hilbert space operators (self-adjoint operators, normal operators, unitary operators, and isometry operators) in terms of operator inequalities.},
	author = {Bouraya, Chaima and Ameur, Seddik}
}
