渐近纠缠算子单值扩张性质的等价性  

The Stability of the Single Valued Extension Property for the Asymptotic Intertwining Operators

作　　者：曹小红[1] 殷俊强[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《数学学报（中文版）》2012年第5期919-928,共10页Acta Mathematica Sinica：Chinese Series

基　　金：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.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.

关 键 词：单值扩张性质 紧摄动 渐近纠缠算子 

分 类 号：O177.2[理学—数学]