Abstract: Let [AlgL] be a CDC-algebra on a Hilbert space [H，]and [φ: AlgL→AlgL] be an additive mapping. This paper proves that if for some positive integer numbers [m,n1,] [φ(am+n+1)=amφ(a)an] hold for all [a∈AlgL,] then there exists some [λ∈Z(AlgL),] such that [φ(a)=λa,] for all [a∈AlgL.]

Key words: additive map, centralizers, CDC-algebra

摘要： 设[AlgL]是Hilbert空间[H]上的一个CDC-代数，[φ:AlgL→AlgL]是一可加映射。证明了如果存在正整数[m,n1]，满足对于任意的[a∈AlgL,]有[φ(am+n+1)=amφ(a)an]，那么存在[AlgL]的中心中的元素[λ∈Z(AlgL)]，使得对于任意的[a∈AlgL,]有[φ(a)=λa]。

关键词: 可加映射, 中心化子, DC-代数