<?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%">On the norm of elementary operatorsin standard operator algebras</style></title><secondary-title><style face="normal" font="default" size="100%">Acta Sci. Math. (Szeged)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2004</style></year></dates><volume><style face="normal" font="default" size="100%">70</style></volume><pages><style face="normal" font="default" size="100%">229-236</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Let A be a complex normed algebra. For A,B ∈ A, define a basic&lt;br&gt;elementary operator MA,B : A → A by MA,B(X) = AXB.&lt;br&gt;Given a standard operator algebra A acting on a complex normed space&lt;br&gt;and A,B ∈ A we have:&lt;br&gt;(i) The lower estimate kMA,B +MB,Ak ≥ 2(√2 − 1)kAkkBk holds.&lt;br&gt;(ii) The lower estimate kMA,B +MB,Ak ≥ kAkkBk holds if&lt;br&gt;inf&lt;br&gt;∈C kA + Bk = kAk or inf&lt;br&gt;∈C kB + Ak = kBk.&lt;br&gt;(iii) The equality kMA,B +MB,Ak = 2kAkkBk holds if&lt;br&gt;kA + Bk = kAk + kBk for some unit scalar .&lt;br&gt;These results extend analogous estimates established earlier for standard&lt;br&gt;operator subalgebras of Hilbert space operators.</style></abstract></record></records></xml>