JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 77-83.doi: 10.6040/j.issn.1671-9352.0.2017.187

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Judgement of a-Weyls theorem and its perturbations

KONG Ying-ying1, CAO Xiao-hong1*, DAI Lei2   

  1. 1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China;
    2. College of Mathematics and Physics, Weinan Normal University, Weinan 714099, Shaanxi, China
  • Received:2017-04-26 Online:2017-10-20 Published:2017-10-12

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Abstract: 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):0N(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.

Key words: approximate point spectrum, a-Weyls theorem, compact perturbation

CLC Number: 

  • O177.2
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