Abstract:

Let R be the field of real numbers and H be a real Hilbert space of dimension at least 2. Let A=H十R be the Spin factor corresponding to H. In this note, we prove that if a bijective map Ø from A onto itself satisfies Ø(x。y)=Ø(x)。Ø(y) for all x,y∈A, and Ø(α+β)=Ø(α)+Ø(β) for all α,β∈R, then there is a unitary operator U on H such that Ø(a+α)=Ua+α for every a∈H, α∈R.

Key words: Spin factor; Jordan multiplicative isomorphism; additivity