Lie Derivations on Banach Algebras

AbstractLet 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 τ on A such that QPD(a)=d(a+P)+τ(a) for all a∈A (where QP 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