Journal of East China Normal University(Natural Science) >

2016 , Vol. 2016 >Issue 6: 111 - 118

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.06.012

The relationship between SVEP and Weyl type theorem under small perturbations

  • DONG Jiong ,
  • CAO Xiao-hong ,
  • LIU Jun-hui
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  • School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China

Received date: 2015-12-21

  Online published: 2017-01-13

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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.

Cite this article

DONG Jiong , CAO Xiao-hong , LIU Jun-hui . The relationship between SVEP and Weyl type theorem under small perturbations[J]. Journal of East China Normal University(Natural Science), 2016 , 2016(6) : 111 -118 . DOI: 10.3969/j.issn.1000-5641.2016.06.012

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