摘要
设N 为Hilbert空间H上的纯原子Nest。首先引进algN上的保谱 可乘映射的定义 ,称映射φ :algNB(H)为保谱 可乘映射 ,若 φ满足 :1°对 A ,B ,C∈algN ,若AB C ∈algN有 φ(AB C)=φ(A) φ(B) φ(C) ;2°δ(φ(T) ) =δ(T)。在此基础上 ,利用秩一算子的性质和Nest代数的特点 ,得到映射 φ的表达式为 :φ(T) =ATA- 1φ(I) , T∈algN 。
Let N be a purely atomic nest on Hilbert space H.By introducing the definition of spectrum-preserving *-multiplicative map on algN,φ:algNB(H) was regarded as a spectrum-preserving *-multiplicative map,if the map φ satisfies following two conditions:(ⅰ) for arbitrary operators A,B and C in algN,when AB *C ∈algN, φ(AB *C)=φ(A)φ(B) *φ(C) was obtained;(ⅱ) δ(φ(T))=δ(T) for arbitrary operator T in algN.On this base,with the help of the properties of rank one operator and the characteristics of nest algebra,the form of φ:φ(T)=ATA -1 φ(I) for every T in algN,where A∈B(H) is obtained,which generalized the results in the refference[3].
基金
湖北省自然科学基金!资助 (99J170 )
湖北省教委重点科研基金!资助 (98A0 19)
