The nonlinear mixed bi-skew Lie triple derivations on ∗-algebras


Jingxuan Wang, Changjing Li, Yueliang Liang, Lin Chen




Let A be a unital *-algebra. In this paper, under some mild conditions on A, it is shown that a map Φ : A → A is a nonlinear mixed bi-skew Lie triple derivation if and only if Φ is an additive *-derivation. As applications, nonlinear mixed bi-skew Lie triple derivations on prime *-algebras, von Neumann algebras with no central summands of type I 1 , factor von Neumann algebras and standard operator algebras are characterized.