<?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 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></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%">Warda Merahi</style></author><author><style face="normal" font="default" size="100%">Said Guedjiba</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A1XA</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language></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%">Warda Merahi</style></author><author><style face="normal" font="default" size="100%">Said Guedjiba</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME PROPERTIES OF COMMON HERMITIAN SOLUTIONS OF MATRIX EQUATIONS A&lt;sub&gt;1&lt;/sub&gt;XA&lt;sup&gt;*&lt;/sup&gt;&lt;sub&gt;1&lt;/sub&gt;= B&lt;sub&gt;1 &lt;/sub&gt;AND A&lt;sub&gt;2&lt;/sub&gt;XA&lt;sup&gt;&amp;lowast;&lt;/sup&gt;&lt;sub&gt;2&lt;/sub&gt; = B&lt;sub&gt;2&lt;/sub&gt;</style></title><secondary-title><style face="normal" font="default" size="100%">MATEMATICKI VESNIK ˇ MATEMATIQKI VESNIK</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%">71</style></volume><pages><style face="normal" font="default" size="100%">214–229</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><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%">Hanane Guelfen</style></author><author><style face="normal" font="default" size="100%">Fuad Kittaneh</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On Numerical Radius Inequalities for Operator Matrices</style></title><secondary-title><style face="normal" font="default" size="100%">Numerical Functional Analysis and Optimization</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%">40</style></volume><pages><style face="normal" font="default" size="100%">1231-1241</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><issue><style face="normal" font="default" size="100%">11</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%">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%">Farida Lombarkia</style></author><author><style face="normal" font="default" size="100%">Amina Boussaid</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Operator equations and inner inverses of elementary operators</style></title><secondary-title><style face="normal" font="default" size="100%"> Linear and Multilinear Algebra </style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2019</style></year></dates><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&amp;nbsp;&lt;i&gt;E&lt;/i&gt;,&lt;i&gt;F&lt;/i&gt;,&lt;i&gt;G&lt;/i&gt;,&lt;i&gt;D&lt;/i&gt;&amp;nbsp;be infinite complex Banach spaces and&amp;nbsp;B(F,E)&amp;nbsp;the Banach space of all bounded linear operators from&amp;nbsp;&lt;i&gt;F&lt;/i&gt;&amp;nbsp;into&amp;nbsp;&lt;i&gt;E&lt;/i&gt;. Consider&amp;nbsp;A1,A2∈B(F,E),&amp;nbsp;B&lt;sub&gt;1&lt;/sub&gt;,B&lt;sub&gt;2&lt;/sub&gt;∈B(D,G)B1,B2∈B(D,G). Let&amp;nbsp;MA1,B1:X→A1XB1&amp;nbsp;be the multiplication operator on&amp;nbsp;B(G,F)&amp;nbsp;induced by&amp;nbsp;A1,B1. In particular,&amp;nbsp;L&lt;sub&gt;A1&lt;/sub&gt;=M&lt;sub&gt;A1&lt;/sub&gt;,&lt;sub&gt;I&lt;/sub&gt;&amp;nbsp;and&amp;nbsp;R&lt;sub&gt;B1&lt;/sub&gt;=M&lt;sub&gt;I,B1&lt;/sub&gt;, where&amp;nbsp;&lt;i&gt;I&lt;/i&gt;&amp;nbsp;is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on&amp;nbsp;B(G,F)B(G,F)&amp;nbsp;is the sum of two multiplication operators Ψ=M&lt;sub&gt;A1,B1&lt;/sub&gt;+M&lt;sub&gt;A2,B2&lt;/sub&gt;. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations&amp;nbsp;M&lt;sub&gt;A1,B1&lt;/sub&gt;(X)=C1 and&amp;nbsp;M&lt;sub&gt;A2,B2&lt;/sub&gt;(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&amp;nbsp;M&lt;sub&gt;A,B&lt;/sub&gt;(X)=C. As a consequence, we obtain well-known results of Daji&lt;sub&gt;c´&lt;/sub&gt;&amp;nbsp;and Koliha.
&lt;/p&gt;
</style></abstract></record></records></xml>