Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (2): 324-331.

• Articles • Previous Articles     Next Articles

Topological Uniform Descent and the Perturbation of Weyl's Theorem

Cui Miaomiao, Cao Xiaohong   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
  • Received:2013-07-30 Revised:2014-10-30 Online:2015-04-25 Published:2015-04-25

Abstract:

An operator T is said to satisfy Browder's theorem if σ(T)\σw(T)⊆π00(T), where σ(T) and σw(T) denote the spectrum and the Weyl spectrum respectively, and π00(T)={λ∈isoσ(T);0N(T-λI)< ∞}. If σ(T)\σw(T)=π00(T), we say T satisfies Weyl's theorem. Using the characteristics of Topological uniform descent domain, the stability of Browder's theorem under compact perturbations is investigated, and those operators which have this stability are characterized.

Key words: Browder's theorem, Compact perturbations, Topological uniform descent

CLC Number: 

  • O177.2
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