Non-linear triple product A*B - B*A derivations on *-algebras

Abstract

Let be a unital prime *-algebra that possesses a nontrivial projection, and let Φ : → be a non-linear map which satisfies Φ(A ◇ B ◇ C) = Φ(A)◇ B ◇ C + A ◇ Φ(B) ◇ C + A ◇ B ◇ Φ(C) for all A, B, C∈, where A ◇ B = A*B - B*A. Then, if Φ(α I⁄2) is self-adjoint map for α∈ {1,i} we show that Φ is additive *-derivation