%A KONG Ying-ying, CAO Xiao-hong, DAI Lei
%T Judgement of a-Weyls 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-Weyls 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-Weyls theorem for operator functional. In addition, we explore the compact perturbation of a-Weyls theorem.