JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (2): 60-65.doi: 10.6040/j.issn.1671-9352.0.2016.038

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Property(z)and Weyl type theorem

DAI Lei1, CAO Xiao-hong2   

  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 710062, Shaanxi, China
  • Received:2016-01-25 Online:2017-02-20 Published:2017-01-18

Abstract: An operator T∈B(X) defined on a Banach space X satisfies property(z), a new variant of Weyls theorem if the complement in the spectrum σ(T) of the upper semi-Weyl spectrum is the set of all isolated points of the approximate point spectrum which are eigenvalues of finite multiplicity. In this note, we first study the conditions between property(z)and other Weyl type theorem, then establish for a bounded linear operator and the calculus defined on a Banach space the sufficient and necessary conditions for which property(z)holds by means of the variant of essential approximate point spectrum. The perturbation of property(z)under finite rank operators is considered.

Key words: property(az), perturbation, spectrum, property(z)

CLC Number: 

  • O177.2
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