完全分配可交换子空间格代数上的中心化映射

摘要

基于Hilbert空间H上的一个完全分配可交换子空间格代数Alg L,考虑Alg L上的中心化映射.设φ为Alg L上的一个可加映射,用完全分配可交换子空间格代数的结构性质和代数分解,证明了:若存在正整数m,n≥1,使得?A∈Alg L,φ(A m+n+1)-A mφ(A)An∈F I成立,则存在Alg L中心里的元素λ,满足?A∈Alg L,有φ(A)=λA.%Based on a completely distributive commutative subspace lattice algebra Alg L on the Hilbert space H ,we considered the centralizer mapping on the Alg L.Let φ:Alg L→Alg L be an additive mapping.By using the structural properties and algebraic decomposition on the completely distributive commutative subspace lattice algebra,we prove that if there are some positive integer numbers m,n ≥ 1,which make ?A ∈ A,φ(Am+n+1 )-A mφ(A )An ∈ FI ,then there exists some elementsλ∈Z (Alg L ),which satisfy ?A∈Alg L,φ(A)=λA.