上三角算子矩阵Weyl型定理的稳定性判定

Judgement on stability of Weyl′s theorem for the upper triangular operator matrices

称算子T满足a-Browder定理,若σa(T)\σea(T)■π00a(T),其中σa(T)和σea(T)分别表示算子T的逼近点谱和本质逼近点谱,和π00a(T)={λ∈isoσa(T),0<dimN(T-λI)<∞}.若σa(T)\σea(T)=π00a(T),则称算子T满足a-Weyl定理.利用上三角算子矩阵中主对角线上的算子的半Fredholm域的特征,研究上三角算子矩阵a-Browder定理和a-Weyl定理在紧摄动下的稳定性.

An operator T is said to satisfy a-Browder′s theorem if σa（T）／σea（T）■π00a（T）,where σa（T） and σea（T） denote the approximate point spectrum and the essential approximate point spectrum,respectively,and π00a（T）={λ∈isoσa（T）,0dimN（T-λI）∞}.If σa（T）／σea（T）=π00a（T）,we say that T satisfies a-Weyl＇s theorem.In this note,by using the characteristics of semi-Fredholm domain of the diagonal of the upper triangular operator matrix,we investigate the stability of a-Browder＇s theorem and a-Weyl＇s theorem for the upper triangular operator matrices under compact perturbations.