Lie derivations on Banach algebras

Let D be a Lie derivation on a unital complex Banach algebra A. Then for every primitive ideal P of A, except for a finite set of them which have finite codimension greater than one, there exist a derivation d from A/P to itself and a linear functional tau On A such that Q(P) D(a) = d(n + P) + tau(a) for all a epsilon A (where Q(P) denotes the quotient map from A onto A/P). Moreover the preceding decomposition holds for all primitive ideals in the case where D is continuous. (C) 2000 Academic Press.