JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (10): 88-94.doi: 10.6040/j.issn.1671-9352.0.2019.729

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Judgement of a-Weyls theorem for bounded linear operators

FENG-GAO Hui-zi, CAO Xiao-hong*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Online:2020-10-20 Published:2020-10-07

Abstract: 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-Weyls theorem if σa(T)\σea(T)=πa00(T), where σa(T) and σea(T) denote the approximate point spectrum and essential approximate point spectrum respectively, and πa00(T)={λ∈iso σa(T):0<n(T-λI)<∞}. A new judgement for the a-Weyls theorem for operators and operator functions is given. Also, the spectrum mapping theorem related to spectrum is considered.

Key words: a-Weyls theorem, approximate point spectrum, essential approximate point spectrum

CLC Number: 

  • O177.1
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