| Wely定理与$(\omega)$性质的等价性 |
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| 引用本文： | 赵玲玲,曹小红,张鹤佳.Wely定理与$(\omega)$性质的等价性[J].数学研究及应用,2011,31(4):705-712. |
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| 作者姓名： | 赵玲玲 曹小红 张鹤佳 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 陕西 西安 710062;陕西师范大学数学与信息科学学院 陕西 西安 710062;陕西师范大学数学与信息科学学院 陕西 西安 710062 |
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| 基金项目： | 教育部新世纪优秀人才支持计划资助项目(Grant No.NCET-06-0870),中央高校基本科研业务费专项资金资助项目(Grant No.GK200901015). |
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| 摘 要： | We call T C B（H） consistent in Fredholm and index （briefly a CFI operator） if for each B ∈ 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 （ω） for T and its conjugate operator T^＊. In addition, the property （ω） for operator matrices is considered.
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| 关 键 词： | Weyl＇s theorem property （ω） spectrum |
| 收稿时间： | 2009/12/24 0:00:00 |
| 修稿时间： | 2010/5/28 0:00:00 |
The Equivalence between Property $(\omega)$ and Weyl's Theorem |
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| Ling Ling ZHAO,Xiao Hong CAO and He Jia ZHANG.The Equivalence between Property $(\omega)$ and Weyl's Theorem[J].Journal of Mathematical Research with Applications,2011,31(4):705-712. |
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| Authors: | Ling Ling ZHAO Xiao Hong CAO and He Jia ZHANG |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China;College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China;College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, P. R. China |
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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. |
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| Keywords: | Weyl's theorem property $(\omega)$ spectrum |
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