<?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. A</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE NUMERICAL RANGE OF ELEMENTARY OPERATORS</style></title><secondary-title><style face="normal" font="default" size="100%">Integr. equ. oper. theory</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2002</style></year></dates><volume><style face="normal" font="default" size="100%">43</style></volume><pages><style face="normal" font="default" size="100%">248-252</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">For n-tuples A = (At, ..., AN) and B = (BI, ..., Bn) of operators on aHilber! space&lt;br&gt;H, let RA,B denote the operator on L(H) defined by RA,B(X) = ~i=1AiX Bi. In&lt;br&gt;this paper we prove that&lt;br&gt;co c~i13i : (a,,..., an) C W(A), (131, ..., 1~) e W(B) C Wo(RA,B)&lt;br&gt;where W is the joint spatial numerical range and W0 is the numerical range. We&lt;br&gt;will show also that this inclusion becomes an equality when I~A,B is taken to be&lt;br&gt;a generalized derivation, and it is strict when RA,B is taken to be an elementary&lt;br&gt;multiplication operator induced by non scalar self-adjoints operators.</style></abstract></record></records></xml>