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中文摘要：
设H是复可分无限维Hilbert空间,B（H）为H上的有界线性算子的全体。Hilbert空间H中一个算子T称作有单值扩张性质（简写为SVEP,记作T∈（SVEP））,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,其中C代表复数集。T∈B（H）称为满足单值扩张性质的紧摄动,若对任意的紧算子K∈K（H）,T＋K满足单值扩张性质。讨论了有界线性算子满足单值扩张性质的紧摄动的判定条件,同时给出了2×2上三角算子矩阵满足单值扩张性质的紧摄动的充要条件。
英文摘要：
Let H be an infinite dimensional separable complex Hilbert space and B（ H） the algebra of all bounded linear operators on H. An operator T∈B（ H） is said to have the single-valued extension property（ SVEP for brevity,write T∈（ SVEP））,if for every open set U■C,the only analytic solution f： U→X of the equation（ T- λI） f（ λ） = 0 for allλ∈U is zero function on U,where C denotes the complex number set. T∈B（ H） is said to have the perturbations of the single valued extension property if T ＋ K have the single-valued extension property for every compact operator K ∈K（ H）. The perturbations of the single valued extension property for bounded linear operators are discussed,and the sufficient necessary condition for is given 2 × 2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.
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