Nonlinear $\ast$-Jordan triple derivation on prime $\ast$-algebras

Abstract

Let 𝒜 be a prime ∗ -algebra and suppose that Φ preserves triple ∗ -Jordan derivation on 𝒜 , that is, for every A , B ∈ 𝒜 , Φ ( A ◇ B ◇ C ) = Φ ( A ) ◇ B ◇ C + A ◇ Φ ( B ) ◇ C + A ◇ B ◇ Φ ( C ) , where A ◇ B = A B + B A ∗ . Then Φ is additive. Moreover, if Φ ( α I ) is selfadjoint for α ∈ { 1 , i } , then Φ is a ∗ -derivation.