深圳大学学报（理工版）2017，Vol.34Issue(4)：372-377,6.DOI:10.3724/SP.J.1249.2017.04372
有界线性算子的a-Weyl定理及亚循环性
A-Weyl's theorem and hypercyclic property for bounded linear operators
摘要
Abstract
Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H.For T ∈ B(H),we call a-Weyl's theorem holds for T if σa(T) \σea(T) =π00(T),where oa (T) and oea (T) denote the approximate point spectrum and essential approximate point spectrum respectively,andπa00(T) ={λ ∈ isoσa(t):0 ＜ dim N(T-λI) ＜ ∞ }.Using the new defined spectrum,we investigate a-Weyl's theorem for operator function.Meanwhile,we characterize the sufficient and necessary conditions for operator function satisfying a-Weyl's theorem if T is a hypercyclic operator.关键词
线性算子理论/a-Weyl定理/逼近点谱/亚循环算子/算子函数/Fredholm算子/谱集/Browder谱Key words
linear operator theory/a-Weyl's theorem/approximate point spectrum/hypercyclic operators/operator function/Fredholm operator/spectrum set/Browder spectrum分类
数理科学引用本文复制引用
杨国增,孔莹莹,曹小红..有界线性算子的a-Weyl定理及亚循环性[J].深圳大学学报（理工版）,2017,34(4):372-377,6.基金项目
国家自然科学基金资助项目(11471200)National Natural Science Foundation of China (11471200) （11471200）
