Nonlinear *-Lie-type derivations on standard operator algebras

Abstract

Let $$\mathcal{H}$$ be an infinite dimensional complex Hilbert space and $$\mathcal{A}$$ be a standard operator algebra on $$\mathcal{H}$$ which is closed under the adjoint operation. It is shown that each nonlinear *-Lie-type derivation δ on $$\mathcal{A}$$ is a linear *-derivation. Moreover, δ is an inner *-derivation as well.