算子矩阵的单值扩张性质的判定

The Judgement of The SVEP and for Operator Matrices

日表示无限维可分的复Hilbert空间，B（H）为日上的有界线性算子的全体．若对于复数域C中任意一个开集矿，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，称算子T具有单值延拓性质（简记为T∈（SVEP））．若对任意一个紧算子K，T＋K都满足单值延拓性质，称T∈B（H）满足单值延拓性质的稳定性．给出了2×2上三角算子矩阵满足单值延拓性质的稳定性的特征．

H denotes a complex separable infinite dimensional Hilbert space. We let B（H） denote 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 short）, denoted by T ∈（SVEP）, if for any 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 the zero function on U. Here C denotes the set of complex numbers. T∈ 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 operatorK. In this paper, we characterize 2 × 2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbatioas.