Abstract
Let R. be a *-ring containing a nontrivial self-adjoint idempotent. In this paper it is shown that under some mild conditions on R, if a mapping d : R -> R. satisfies
d([U*, V]) = [d(U)*, V] + [U*, d(V)]
for all U, V is an element of R., then there exists Z(U,V) is an element of R(Z) (depending on U and V), where Z(R) is the center of R, such that d(U + V) = d(U) + d(V) + Z(U,V). Moreover, if R is a 2-torsion free prime *-ring additionally, then d = psi +xi, where psi is an additive *-derivation of R. into its central closure T and xi is a mapping from R. into its extended centroid C such that xi(U + V) = xi(U) + xi(V) + Z(U,V) and xi([U, V]) = 0 for all U, V is an element of R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras.