MAPS PRESERVING STRONG SKEW LIE PRODUCT ON FACTOR VON NEUMANN ALGEBRAS  

作　　者：崔建莲 Choonkil Park 

机构地区：[1]Department of Mathematical Sciences,Tsinghua University [2]Department of Mathematics,Hanyang University,Seoul 133-791,Republic of Korea

出　　处：《Acta Mathematica Scientia》2012年第2期531-538,共8页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(10871111);the Specialized Research Fund for Doctoral Program of Higher Education(200800030059)(to Cui);Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(NRF-2009-0070788)(to Park)

摘　　要：Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a linear bijective map ψA →A satisfying ψ（A）ψ（B） - ψ（B）ψ（A）＊ = AB - BA＊ for A, B ∈ A and a real functional h on A with h（0） -= 0 such that Ф（A） = ψ（A） ＋ h（A）I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф（A） = cA ＋ h（A）I for every A ∈ .4, where c = ±1.Let A be a factor von Neumann algebra and Ф be a nonlinear surjective map from A onto itself. We prove that, if Ф satisfies that Ф（A）Ф（B） - Ф（B）Ф（A）＊ -- AB - BA＊ for all A, B ∈ A, then there exist a linear bijective map ψA →A satisfying ψ（A）ψ（B） - ψ（B）ψ（A）＊ = AB - BA＊ for A, B ∈ A and a real functional h on A with h（0） -= 0 such that Ф（A） = ψ（A） ＋ h（A）I for every A ∈ A. In particular, if .4 is a type I factor, then, Ф（A） = cA ＋ h（A）I for every A ∈ .4, where c = ±1.

关 键 词：Skew Lie product factor yon Neumann algebras preserver problems 

分 类 号：O153[理学—数学]