上三角算子矩阵的单值延拓性质的摄动  

The Perturbation of the Single Valued Extension Property for Upper Triangular Operator Matrices

作　　者：曹小红[1] 吴学俪 张敏[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）》2016年第4期451-460,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11371012;11471200;11571213);陕西师范大学中央高校基本科研业务费专项资金资助项目(GK201601004)

摘　　要：设H为无限维可分的复Hilbert空间,B(H)为H上的有界线性算子全体.算子T∈B(H)称为具有单值延拓性质,若对任意一个开集U(?)C,满足方程(T-λI)f(λ)=0(任给λ∈U)的唯一的解析函数f:U→H为零函数;T∈B(H)称为满足单值延拓性质的稳定性,若对任意一个紧算子K∈B(H),T+K都满足单值延拓性质.本文给出了2×2上三角算子矩阵在紧摄动下满足单值延拓性质的稳定性的特征.Let H be an infinite-dimensional separable complex Hilbert space and B（H） be the algebra of all bounded linear operators on H. An operator T∈ B（H） is said to have the single-valued extension property, if for every open set U C C, the only analytic solution f ： U → H of the equation （T - λI）f（λ） = 0 for all ）λ∈ U is zero function on U; T E B（H） is said to have the stability of the single-valued extension property if T ＋ K has the single-valued extension property for any compact operator K ∈ B（H）. In this paper, we characterize 2 × 2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.

关 键 词：单值延拓性质 紧摄动 谱 

分 类 号：O177.2[理学—数学]