<?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 some operator norm inequalities</style></title><secondary-title><style face="normal" font="default" size="100%">Linear Algebra Appl.</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%">389</style></volume><pages><style face="normal" font="default" size="100%">183-187</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&lt;br&gt;∗-algebra of all bounded linear operators on a complex Hilbert space&lt;br&gt;H, S be an invertible and selfadjoint operator in B(H) and let (I, .&lt;br&gt;I ) denote a norm ideal&lt;br&gt;of B(H). In this note, we shall show the following inequality:&lt;br&gt;∀X ∈ I : SXS&lt;br&gt;−1 − S&lt;br&gt;−1XS&lt;br&gt;I  (SS&lt;br&gt;−1 − 1)SXS&lt;br&gt;−1 + S&lt;br&gt;−1XS&lt;br&gt;I .</style></abstract></record></records></xml>