Abstract:

Let M be a factor von Neumann algebra acting on a complex separable Hilbert spaceM with dim M>2, and Φ be a linear bijective map from M onto itself.  We prove that  Φ satisfies Φ(A)Φ(B)=Φ(B)Φ(A)* whenever AB=BA* for all A,B∈M if and only if  Φ(A)=λΨ(A) for all A∈M, where λ is a nonzero real number and Ψ is an atomorphism of  M

Key words: linear preserver; zero of polynominal; von Neumann algebra