Nonlinear centralizers on factor von Neumann algebras
YANG Cui1， WU Bing1， LIU Zhen 2
1.School of Information Technology， Hebei Polytechnic Institute， Shijiazhuang 050091， China；2.School of Mathematics and Statistics， Kashgar University， Kashgar， Xinjiang 844000， China
Abstract：Let m，n be non-zero integers with (m＋n)(m－n)≠0， M be a factor von Neumann algebra on Hilbert spaces H over the real or complex field F and φ be a nonlinear map from M into itself. By using the algebraic decomposion on M， it is showed that if φ satisfies 2mφ(AB)＋2nφ(BA)＝mφ(A)B＋mAφ(B)＋nφ(B)A＋nBφ(A) for all A，B∈M， then the map is an additive centralizer and we characterize the concrete form： there exists a λ∈F such that φ：A→λA for all A∈M.
2020, Vol. 54 
