算子摄动与谱值映射的连续性

On Perturbation and Continuity of Spectral Valued Map for Linear Bounded Operators on Hilberts Space

讨论 Hibert空间上有界线性算子摄动和谱值映射的连续性问题 .得到 σk(.)一类子集上半连续的充要条件和 H∞∞ (.)连续的充要条件 ,推广了文 [7]主要结果 .

In this paper, we study perturbation and continuity of spectral valued map for linear bounded operators on Hilbert space. We obtain sufficient and necessary conditions of continuity of F(·) , which is a subset of σ k(·), and sufficient and necessary conditions of continuity of H ∞∞ (·).