At The Reversible Yuan.vn Algebra Differentiable Mapping Characteristics And The Jordan On The Spin Factor Can Take Isomorphism

Let M be a vN algebra on an infinite-dimensional complex Hilbert space H.Z∈M, ψ is a derivable mapping at Z only if ψ is a linear mapping and ψ(ST)=ψ(S)T+Sψ(T)for any S,t∈M with ST=Z.Let Z∈M be an invertible element,in this paper the result that ψ is a derivable mapping at I which is the unit of M,so ψ is an inner derivation,is proved provided that ψ is a norm-continuous derivable mapping at Z on M.Let R be the field of real numbers and H be a real Hilbert space of dimension at least2.Let A=H(?)R be the Spin factor conesponding to H.In this note,it is proved that if a bijective map φ from A onto itself satisfiesφ(x(?)y)=φ(x)(?)φ(y)for all x,y∈A, and φ(α+β)=φ(α)+φ(β)for all α,β∈R,then there is a unitary operate U on H such thatφ(a+α)=Ua+α for every a∈H,α∈R.