<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ameur, Seddik</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SELFADJOINT OPERATORS, NORMAL OPERATORS, AND CHARACTERIZATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Operators and MatricesOperators and Matrices</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2019</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">3</style></number><volume><style face="normal" font="default" size="100%">13</style></volume><pages><style face="normal" font="default" size="100%">835–842</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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&amp;nbsp;=&amp;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&amp;nbsp;=&amp;gt;2||SXS||,(S ∈ B(H)), (ii) S*DSS = 0 = SDSS*,(S ∈ B(H)), (iii) S*DSS=&amp;gt; 0 =&amp;gt;SDSS*,(S ∈ B(H)). &amp;nbsp;</style></abstract></record></records></xml>