Property $(\omega')$ and Its Perturbation
Received:December 06, 2009  Revised:April 26, 2010
Key Words: property $(\omega')$   spectrum   Weyl's theorem.  
Fund Project:Supported by the Fundamental Research Funds for the Central Universities (Grant No.GK200901015) and the Plan of The New Century Talented Person of the Ministry of Education of China.
Author NameAffiliation
Yan Hua ZHANG College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China 
Xiao Hong CAO College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China 
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Abstract:
      In this note we define the property $(\omega')$, a variant of Weyl's theorem, and establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for which property $(\omega')$ holds by means of the variant of the essential approximate point spectrum $\sigma_{1}(\cdot)$ and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property $(\omega')$ is discussed.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.05.014
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