CHARACTERIZATION OF SOME NON-ADDITIVE MIXED BISKEW JORDAN TYPE DERIVATIONS ON ∗-RINGS

Abstract

Let F be a 2-torsion free ∗-ring having a unital element and a non-trivial symmetric idempotent. In the present paper, we demonstrate that, under certain mild conditions, if a map Ψ : F → F (not necessarily additive) satisfies Ψ(U♢K ◦L)=Ψ(U)♢K ◦L +U♢Ψ(K)◦L +U♢K ◦Ψ(L) for all U ,K ,L ∈ F, then Ψ is an additive ∗-derivation. Particularly, we apply our main result to certain special classes of ∗-algebras such as prime ∗-algebra, von Neumann algebras with no central summands of type I1 and standard operator algebras.