| Property $(\omega)$ and Its Perturbations |
| Received:December 30, 2010 Revised:December 19, 2011 |
| Key Words:
property $(\omega)$ perturbation consistency in Fredholm and index.
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| Fund Project:Supported by the Fundamental Research Funds for the Central Universities (Grant No.GK200901015). |
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| Abstract: |
| In the note, we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property $(\omega)$ by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and index. In addition, the stability of property $(\omega)$ for $H(P)$ operators is considered. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.04.009 |
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