| Property $(\omega')$ and Its Perturbation |
| Received:December 06, 2009 Revised:April 26, 2010 |
| Key Words:
property $(\omega')$ spectrum Weyl's theorem.
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| 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. |
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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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