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 doi:

DOI: 10.3724/SP.J.1249.2017.04372

Journal of Shenzhen University Science and Engineering (深圳大学学报理工版) 2017/34:4 PP.372-377

## A-Weyl's theorem and hypercyclic property for bounded linear operators

• Yang Guozeng 1   Kong Yingying 2   Cao Xiaohong 2
• 1.School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, Henan Province, P. R. China;
• 2.Shaanxi Normal University, Institute of Mathematics and Information Science, Xi'an 710062, Shaanxi Province, P. R. China

Abstract：
Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. For TB(H), we call a-Weyl's theorem holds for T if σa(T)σea(T)=π00a(T), where σa(T) and σea(T) denote the approximate point spectrum and essential approximate point spectrum respectively, and π00a(T)={λ∈isoσa(t):0N(T-λI)<∞}. Using the new defined spectrum, we investigate a-Weyl's theorem for operator function. Meanwhile, we characterize the sufficient and necessary conditions for operator function satisfying a-Weyl's theorem if T is a hypercyclic operator.

Key words：linear operator theory,a-Weyl's theorem,approximate point spectrum,hypercyclic operators,operator function,Fredholm operator,spectrum set,Browder spectrum

ReleaseDate：2017-10-20 02:07:26

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