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渐近纠缠算子单值扩张性质的等价性
引用本文:曹小红,殷俊强.渐近纠缠算子单值扩张性质的等价性[J].数学学报,2012(5):919-928.
作者姓名:曹小红  殷俊强
作者单位:陕西师范大学数学与信息科学学院
基金项目:陕西师范大学中央高校基本科研业务费专项资金资助(GK200901015)
摘    要:算子T∈B(H)称作有单值扩张性质,若对任意一个开集U■C,满足方程(T-λI)f(λ)=0(λ∈U)的唯一的解析函数为零函数.显然,当int σ_p(T)=时,T有单值扩张性质,其中σ_p(T)为T的点谱.本文给出了渐近纠缠算子单值扩张性质的稳定性的等价条件,同时研究了2×2上三角算子矩阵的单值扩张性质的稳定性.

关 键 词:单值扩张性质  紧摄动  渐近纠缠算子

The Stability of the Single Valued Extension Property for the Asymptotic Intertwining Operators
Xiao Hong CAO Jun,Qiang YIN.The Stability of the Single Valued Extension Property for the Asymptotic Intertwining Operators[J].Acta Mathematica Sinica,2012(5):919-928.
Authors:Xiao Hong CAO Jun  Qiang YIN
Institution:College of Mathematics and Information Science,Shaanxi Normal University, Xi,an 710062,P.R.China
Abstract:An operator T∈B(H) is said to have the single-valued extension property, if for every open set U■C,the only analytic solution f:U→X of the equation (T -λI)f(λ) = 0 for all λ∈U is zero function on U.Clearly the point spectrum of any operator which has empty interior must have the single-valued extension property. In this paper,we investigate the stability of the single-valued extension property under compact perturbations for the Asymptotic Intertwining operator.Also,we characterize 2×2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.
Keywords:single-valued extension property  compact perturbations  asymptotic Intertwining operator
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