Journal of East China Normal University(Natural Sc

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The relationship between SVEP and Weyl type theorem under small perturbations

DONG Jiong, CAO Xiao-hong, LIU Jun-hui   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China
  • Received:2015-12-21 Online:2016-11-25 Published:2017-01-13

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)\σω(T)=π00(T),  where σ(T) and σω(T) denote the spectrum and the Weyl spectrum of T respectively, π00(T)={λ ∈ isoσ(T): 0<dim N(T-λI)<∞}. If σ(T)\σω(T)   π00(T),  T is called satisfying Browder’s theorem. In this paper, using the property of generalized Kato decomposition, we explore the relation between the single-valued extension property and Weyl’s theorem under small compact perturbations.