Characterizations of *-Lie derivable mappings on prime *-rings

Sa？etak 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 ∈ R, then there exists ZU,V ∈ Z(R) (depending on U and V), where Z(R) is the center of R, such that d(U + V) = d(U) + d(V) + ZU,V. Moreover, if R is a 2-torsion free prime *-ring additionally, then d = ψ + ξ, where ψ is an additive *-derivation of R into its central closure T and ξ is a mapping from R into its extended centroid C such that ξ(U + V) = ξ(U) + ξ(V) + ZU,V and ξ([U, V]) = 0 for all U, V ∈ R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras