%A FENG-GAO Hui-zi, CAO Xiao-hong
%T Judgement of a-Weyls theorem for bounded linear operators
%0 Journal Article
%D 2020
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2019.729
%P 88-94
%V 55
%N 10
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3353.shtml}
%8 2020-10-20
%X Let *H* be an infinite dimensional separable complex Hilbert space and *B(H)* be the algebra of all bounded linear operators on *H. T∈B(H)* satisfies the a-Weyls theorem if *σ*_{a}*(T)\σ*_{ea}*(T)=π*^{a}_{}00*(T)*, where *σ*_{a}*(T)* and *σ*_{ea}*(T)* denote the approximate point spectrum and essential approximate point spectrum respectively, and *π*^{a}_{}00*(T)={λ*∈iso *σ*_{a}(*T)*:0<*n(T-λI)*<∞}. A new judgement for the a-Weyls theorem for operators and operator functions is given. Also, the spectrum mapping theorem related to spectrum is considered.