WANG Meili 1,2, JI Guoxing 1*
(1 School of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China；2 College of Science, Xi′an University of Science and Technology, Xi′an 710054, Shaanxi, China)
Abstract:
Let H and K be complex Hilbert spaces and let A and B be two factor von Neumannalgebras acting on H and K respectively with dimensions greater than one.Assume that Φ:A→B is a bijective map satisfying Φ（A*B-ξB*A)=Φ(A)*Φ(B)-ξΦ(B)*Φ(A) for all A,B∈A.It is proved that,(1)if ξ=0,then Φ is a linear or a conjugate linear *-isomorphism;(2)if ξ∈R/{0,1,-1} and Φ is unital, then Φ is a linear or a conjugate linear *-isomorphism;(3) if ξ∈C/R and Φ is unital, then Φ is a linear *-isomorphism.
KeyWords:
factor von Neumann algebra; Lie product; *-isomorphism
