<?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%">Sur I&amp;rsquo;lmage et le Noyau d&amp;rsquo;une Dbrivation G6n6ralis6e</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%">1998</style></year></dates><volume><style face="normal" font="default" size="100%">274</style></volume><pages><style face="normal" font="default" size="100%">77~83</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Let A E_Y(H~), B E_F(H.J ( w h ere Hi, H, are Hilbert spaces), and let S,, H&lt;br&gt;denote the operator on _Y( H,, H,) given by&lt;br&gt;6,,,(X) = AX - XB, X =.Y( H,, H,)&lt;br&gt;J. P. Williams asked: For which A is R(i%,)-n {A*) = {O}?(w here S,, A = 6,) We&lt;br&gt;obtain some operators in this class. The case of 6, s, A f B, is interesting in itself;&lt;br&gt;moreover it is useful if we have to use a decomposition of the Hilbert space in a direct&lt;br&gt;some for the consideration of 6,. In this note we describe some classes of operators&lt;br&gt;A, B for which we have R(6,, H) - f? ker S,,, se = (0). 0 1998 Elsevier Science</style></abstract></record></records></xml>