The Equivalence between Property $(\omega)$ and Weyl's Theorem |
Received:December 24, 2009 Revised:May 28, 2010 |
Key Words:
Weyl's theorem property $(\omega)$ spectrum.
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Fund Project:Supported by Plan of the New Century Talented Person of the Ministry of Education of China (Grant No.NCET-06-0870) and the Fundamental Research Funds for the Central Universities (Grant No.GK200901015). |
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Abstract: |
We call $T\in B(H)$ consistent in Fredholm and index (briefly a CFI operator) if for each $B\in B(H)$, $TB$ and $BT$ are Fredholm together and the same index of $B$, or not Fredholm together. Using a new spectrum defined in view of the CFI operator, we give the equivalence of Weyl's theorem and property $(\omega)$ for $T$ and its conjugate operator $T^*$. In addition, the property $(\omega)$ for operator matrices is considered. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2011.04.016 |
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