JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (10): 82-87.doi: 10.6040/j.issn.1671-9352.0.2018.134

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Judgement of Weyls theorem for bounded linear operators

ZHANG Ying1, CAO Xiao-hong1*, DAI Lei2   

  1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China;
    2. College of Mathematics and Physics, Weinan Normal University, Weinan 714000, Shaanxi, China
  • Received:2018-03-20 Online:2018-10-20 Published:2018-10-09

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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 Weyls theorem if σ(T)\σw(T)=π00(T), where σ(T) and σw(T) denote the spectrum and the Weyl spectrum respectively, π00(T)={λ∈iso σ(T):0An operator T∈B(H) is said to have the single-valued extension property, if for every open set U⊆C, the only analytic solution of the equation (T-λI)f(λ)=0(for all λ∈U)is zero function on U. Using the single-valued extension property, we give a new judgement for Weyls theorem.

Key words: spectrum, single-valued extension property, Weyls theorem

CLC Number: 

  • O177.2
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