Nonlinear maps preserving the mixed Jordan type products on *-algebras.

AbstractSuppose R and C represent two unital *-algebras, with R containing a nontrivial projection. In the present article, we demonstrate, under certain restrictions that if a bijective map Δ:R→C satisfies Δ(K°N•W)=Δ(K)°Δ(N)•Δ(W) for all K,N,W∈R, then Δ is a *-preserving ring isomorphism. Also, this result is investigated in factor von Neumann algebras. [ABSTRACT FROM AUTHOR]