| Property $(\omega_1)$ and Single Valued Extension Property |
| Received:December 17, 2008 Revised:June 30, 2009 |
| Key Words:
property $(\omega_1)$ single valued extension property.
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| Fund Project:Supported by the Fundamental Research Funds for the Central Universities (Grant No.GK200901015) and the Innovation Funds of Graduate Programs, SNU (Grant No.2009cxs028). |
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| Abstract: |
| In this note we study the property $(\omega_1)$, a variant of Weyl's theorem by means of the single valued extension property, and establish for a bounded linear operator defined on a Banach space the necessary and sufficient condition for which property $(\omega_1)$ holds. As a consequence of the main result, the stability of property $(\omega_1)$ is discussed. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.008 |
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