Nonlinear *-Jordan-type derivations on *-algebras

Abstract

Let 𝒜 be a unital ∗-algebra with the unit I. Assume that 𝒜 contains a nontrivial projection P which satisfies X𝒜P=0 implies X=0 and X𝒜(I−P)=0 implies X=0. In this paper, it is shown that Φ is a nonlinear ∗-Jordan-type derivation on 𝒜 if and only if Φ is an additive ∗-derivation. As applications, the nonlinear ∗-Jordan-type derivations on prime ∗-algebras, von Neumann algebras with no central summands of type I1, factor von Neumann algebras and standard operator algebras are characterized.