A NOTE ON NONLINEAR MIXED TYPE PRODUCT [E ⋄ K, D]∗ ON ∗-ALGEBRAS

Abstract

Let B be a ∗-algebra with the unity and a nontrivial projection. In the present paper, we show under certain restrictions that if a map Ψ : B →B satisfies Ψ([E ⋄ K, D]∗) = [Ψ(E) ⋄ K, D]∗ + [E ⋄Ψ(K), D]∗ + [E ⋄ K, Ψ(D)]∗ for all E, K, D ∈ B, then Ψ is an additive ∗-derivation.