Let A and B be two unital C∗-algebras. We consider the surjective maps φ : A → B which satisfy φ(|A + B|) = |φ(A) + φ(B)| for every A, B ∈ A, where A is a C∗-algebra of real rank zero. We show that all these maps are linear or antilinear ∗-homomorphism multiplied by a central element.
