%A KONG Ying-ying, CAO Xiao-hong, DAI Lei %T Judgement of a-Weyls theorem and its perturbations %0 Journal Article %D 2017 %J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) %R 10.6040/j.issn.1671-9352.0.2017.187 %P 77-83 %V 52 %N 10 %U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_2620.shtml} %8 2017-10-20 %X Let H be an infinite dimensional separable complex Hilbert space and B(H) 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)\σaw(T)=πa00(T), where σa(T)and σaw(T)denote the approximate point spectrum and essential approximate point spectrum respectively, and πa00 (T)={λ∈iso σa(T):0<dim N(T-λI)<∞}. Using the new spectrum defined in this paper, we investigate a-Weyls theorem for operator functional. In addition, we explore the compact perturbation of a-Weyls theorem.