@article {16336,
	title = {Sur I\&rsquo;lmage et le Noyau d\&rsquo;une Dbrivation G6n6ralis6e},
	journal = {Linear Algebra Appl.},
	volume = {274},
	year = {1998},
	pages = {77~83},
	abstract = {Let A E_Y(H~), B E_F(H.J ( w h ere Hi, H, are Hilbert spaces), and let S,, Hdenote the operator on _Y( H,, H,) given by6,,,(X) = AX - XB, X =.Y( H,, H,)J. P. Williams asked: For which A is R(i\%,)-n {A*) = {O}?(w here S,, A = 6,) Weobtain some operators in this class. The case of 6, s, A f B, is interesting in itself;moreover it is useful if we have to use a decomposition of the Hilbert space in a directsome for the consideration of 6,. In this note we describe some classes of operatorsA, B for which we have R(6,, H) - f? ker S,,, se = (0). 0 1998 Elsevier Science},
	author = {Seddik. A}
}
