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A-Weyl’s theorem and hypercyclic property for bounded linear operators(PDF)

《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

Issue:
2017年No.4(331-440)
Page:
372-377
Research Field:
数学与应用数学
Publishing date:

Info

Title:
A-Weyl’s theorem and hypercyclic property for bounded linear operators
Author(s):
Yang Guozeng1 Kong Yingying2 and Cao Xiaohong2
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
Keywords:
linear operator theory a-Weyl’s theorem approximate point spectrum hypercyclic operators operator function Fredholm operator spectrum set Browder spectrum
PACS:
O 177.2
DOI:
10.3724/SP.J.1249.2017.04372
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 T∈B(H), we call a-Weyl’s theorem holds for T if σa(T)\σea(T)=πa00(T), where σa(T) and σea(T) denote the approximate point spectrum and essential approximate point spectrum respectively, and πa00(T)={λ∈isoσa(t)∶0<dim N(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.

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Last Update: 2017-06-26