Nonlinear maps preserving the mixed triple η-*-product on von Neumann algebras
ZHANG Fangjuan1， ZHU Xinhong2
(1.School of Science， Xi'an University of Posts and Telecommunications， Xi'an 710121， China； 2. Xi'an Modern Control Technology Institute， Xi'an 710065， China)
Abstract：Let η∈0,1}， and let M and N be two von Neumann algebras， one of which has no central abelian projections. A nonlinear bijective map ：M→N has been demonstrated to satisfy ([A，B]*(η)·ηC)＝[(A)，(B)]*(η)·η(C) for all A，B，C∈M. If η＝－1， then (I) is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism， where (I) is a self-adjoint central element with (I)2＝I. If η≠－1 and satisfies (I)＝I，(iI)*＝－(iI)， then one of the following statements holds： 1) If |η|＝1， then is a linear *-isomorphism. 2) If |η|≠1， then is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism.
2022, Vol. 56 
