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| Property (ω′) and Its Perturbation | |
| 基金项目： | Supported by the Fundamental Research Funds for the Central Universities (Grant No. GK200901015); the Plan of The New Century Talented Person of the Ministry of Education of China |
| 摘 要： | In this note we define the property (ω′), 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 (ω′) holds by means of the variant of the essential approximate point spectrum σ1(·) and the spectrum defined in view of the property of consistency in Fredholm and index. In addition, the perturbation of property (ω′) is discussed. |
| 关 键 词： | property (ω′) spectrum Weyl’s theorem. |
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