<?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%">Seddik Ameur</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 Matrices</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><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%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	Let B(H) be the C&lt;sup&gt;∗&lt;/sup&gt; -algebra of all bounded linear operators acting on a complex separable Hilbert space H . We shall show that:
&lt;/p&gt;

&lt;p style=&quot;text-align: justify;&quot;&gt;
	1. The class of all selfadjoint operators in B(H) multiplied by scalars is characterized by ∀X ∈ B(H), S&lt;sup&gt;2&lt;/sup&gt;X +XS&lt;sup&gt;2&lt;/sup&gt;&amp;nbsp;=&amp;gt;2||SXS||, (S ∈ B(H)).
&lt;/p&gt;

&lt;p style=&quot;text-align: justify;&quot;&gt;
	2. The class of all normal operators in B(H) is characterized by each of the three following properties (where DS = S&lt;sup&gt;∗&lt;/sup&gt;S−SS&lt;sup&gt;∗&lt;/sup&gt; , for S ∈ B(H)),
&lt;/p&gt;

&lt;p style=&quot;text-align: justify;&quot;&gt;
	(i) ∀X ∈ B(H), S&lt;sup&gt;2&lt;/sup&gt;X + XS&lt;sup&gt;2&lt;/sup&gt;&amp;nbsp;=&amp;gt;2||SXS||,(S ∈ B(H)),
&lt;/p&gt;

&lt;p style=&quot;text-align: justify;&quot;&gt;
	(ii) S∗DSS = 0 = SDSS∗,(S ∈ B(H)),
&lt;/p&gt;

&lt;p style=&quot;text-align: justify;&quot;&gt;
	(iii) S&lt;sup&gt;∗&lt;/sup&gt;D&lt;sub&gt;S&lt;/sub&gt;S=&amp;gt; 0 =&amp;gt;SD&lt;sub&gt;S&lt;/sub&gt;S&lt;sup&gt;∗&lt;/sup&gt;,(S ∈ B(H)).
&lt;/p&gt;

&lt;p style=&quot;text-align: justify;&quot;&gt;
	&amp;nbsp;
&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue></record><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%">Chaima Bouraya</style></author><author><style face="normal" font="default" size="100%">Seddik Ameur</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the characterizations of some distinguished subclasses of Hilbert space operators</style></title><secondary-title><style face="normal" font="default" size="100%">Acta Scientiarum Mathematicarum</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><volume><style face="normal" font="default" size="100%">84</style></volume><pages><style face="normal" font="default" size="100%">611-627</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p style=&quot;text-align: justify;&quot;&gt;
	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.
&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">34</style></issue></record></records></xml>