Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1500-1506.

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The Stability of the Weyl Type Theorem

 TIAN Jun-Hong1, CAO Xiao-Hong2, DAI Lei3   

  1. 1.College of Mathematica and Sta., Tianshui Normal University, Tianshui, 741001;
    2.College of Mathematica and |Information Science, |Shaanxi Normal University, Xi'an 710060;
    3.College of Mathematica |and |Information |Science, Weinan Normal University, |Weinan |714099
  • Received:2012-12-24 Revised:2014-05-19 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    陕西省自然科学基金(2014JQ1015)、渭南市科技计划项目(2013KYJ-1)和天水师范学院中青年教师科研资助项目(TS201205)资助

Abstract:

A Hilbert space operator T is said to satisfy a-Browder's theorem if σa(T)\σawa00(T), where σa(T) and σaw(T) denote the approximate point spectrum and the Weyl essential approximate point spectrum respectively, and πa00(T)={λiso σa(T), 0N(T-λI)<∞}. If σa(T)\σaw(T)=πa00(T), we say T satisfies a-Weyl's theorem.TB(H) is said to have the stability of the a-Browder's (a-Weyl's) theorem if T+K satisfies the a-Browder's (a-Weyl's) theorem for all compact operators K. In this note, we investigate the stability of the a-Browder's theorem and the a-Weyl's theorem, and we characterize those operators for which the a-Browder's theorem and the a-Weyl's theorem are stable under compact perturbations.

Key words: a-Browder´s theorem, a-Weyl´s theorem, Compact perturbation

CLC Number: 

  • 47A55
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