| 左飞,申俊丽.代数κ-拟-A类算子的Weyl定理[J].数学年刊A辑,2011,32(4):459~466 |
| 代数κ-拟-A类算子的Weyl定理 |
| Weyl’s Theorem for Algebraically k-Quasi-Class A Operators |
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| DOI： |
| 中文关键词: Weyl定理 Browder定理 代数κ-拟-A类算子 a-Weyl定理 a-Browder定理 |
| 英文关键词: |
| 基金项目:教育部科技司(No208081)资助的项目 |
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| 中文摘要: |
| 若$T$或$T^{*}$是无穷维可分的Hilbert空间$H$上的代数$k$-拟-\!$A$类算子, 则Weyl定理对任意的$f \in H(\sigma(T))$成立,
其中 $H(\sigma(T))$为$\sigma (T)$ 的开邻域上解析函数的全体.若$T^{*}$是代数$k$-拟-\!$A$类算子,
则$a$-Weyl定理对$f(T)$成立. 还证明了若$T$或$T^{*}$是代数$k$-拟-\!$A$类算子,
则Weyl谱与本质近似点谱的谱映射定理对$f(T)$成立. |
| 英文摘要: |
| If $T$ or $T^{*}$ is an algebraically $k$-quasi-class $A$ operator acting on an infinitely dimensional separable Hilbert space $H$,
then it is proved that the Weyl's theorem holds for every $f \in H (\sigma(T))$, where $H (\sigma(T))$ denotes the
set of all analytic functions on an open neighborhood of $\sigma(T).$ Moreover, if $T^{*}$ is an algebraically
$k$-quasi-class $A$ operator, then the $a$-Weyl's theorem holds for $f(T)$. Also, if $T$ or $T^{*}$ is an algebraically
$k$-quasi-class $A$ operator, then the spectral mapping theorems for both the Weyl's spectrum
and the essential approximate point spectrum of $T$ are established for every $f(T)$. |
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