JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 55-61.doi: 10.6040/j.issn.1671-9352.0.2019.099

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Property(ω1)and the single-valued extension property

DAI Lei1, HUANG Xiao-jing1, GUO Qi2   

  1. 1. School of Mathematics and Physics, Weinan Normal University, Weinan 714099, Shaanxi, China;
    2. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: A bounded linear operator T satisfies property(ω1), if the complement in the approximate point spectrum σa(T)of the upper semi-Weyl spectrum σea(T)is contained in the set of all isolated points of the spectrum σ(T)which are finite eigenvalues. In this paper, by means of the new spectrum defined in view of the single-valued extension property, the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space satisfying the property(ω1)are established. As an application, the property(ω1)for hypercyclic(or supercyclic)operators are characterised.

Key words: property(ω1), single-valued extension property, hypercyclic operator, supercyclic operator, spectrum

CLC Number: 

  • O177.2
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