完全分配可交换子空间格代数上的广义Jordan中心化映射

Generalized Jordan centralizer mapping on completely distributive commutative subspace lattice algebras

基于Hilbert空间H上的一个完全分配可交换子空间格L,讨论L上的代数Alg L上的中心化映射。设Φ为Alg L上的一个可加映射,运用完全分配可交换子空间格代数的结构性质和代数分解,证明若存在正整数m、n、r≥1,使得?A∈Alg L,有(m+n)Φ(A^(r+1))-(mΦ(A)A^r+nA^rΦ(A))∈Z(Alg L),则存在Alg L的中心元素λ∈Z(Alg L),满足?A∈Alg L,有Φ(A)=λA。

Based on a completely distributive commutative subspace lattice L on a Hilbert H,the centralizer mapping on the completely distributive commutative subspace lattice algebras Alg Lis discussed.LetΦ：Alg L→Alg L be an additive mapping.According to the structural properties and algebraic decomposition on the completely distributive commutative subspace lattice algebras,it is proved that if there are some positive integer numbers m,n,r≥1,such that A∈Alg L,（m＋n）Φ（A^r＋1）-（mΦ（A）A^r＋nA～rΦ（A））∈Z（Alg L）,then there exists someλ∈Z（Alg L）,which satisfies A∈Alg L,Φ（A）=λA.