Additivity of Jordan maps on standard Jordan operator algebras

Let A   be a standard Jordan operator algebra on a Hilbert space of dimension >1>1 and B   be an arbitrary Jordan algebra. In this note, we prove that if a bijection ϕ:A→Bϕ:A→B satisfiesϕ(a∘b)=ϕ(a)∘ϕ(b)for alla,b∈A,where ∘∘ is the special Jordan product on A  , then ϕϕ is additive.