论文标题
Weyl的定理用于通勤超自然现象和$ \ ast $ -Parantormal Operators
Weyl's theorem for commuting tuple of paranormal and $\ast$-paranormal operators
论文作者
论文摘要
在本文中，我们表明，$ \ ast $ \ ast $ -paranormal运算符的通勤对$ t =（t_1，t_2）$ $ t_1 $ t_1 $和$ t_2 $与quasitriangular属性满足Weyl theorem-i的满足通勤一对超自然操作员满足Weyl的定理-II，即$$σ_t（t）\setMinusΩ（t）=π_{00}（t），$σ_t（t），\，\，σ_，σ_频谱，泰勒魏尔光谱，关节韦尔谱和集合分别由$ t $的隔离特征值组成，分别具有有限的多重性。 此外，我们证明Weyl的定理II以$ f（t）$持有，其中$ t $是通勤对的超自然运算符，$ f $是$σ_T（t）$的社区中的一个分析功能。
In this article, we show that a commuting pair $T=(T_1,T_2)$ of $\ast$-paranormal operators $T_1$ and $T_2$ with quasitriangular property satisfy the Weyl's theorem-I, that is $$σ_T(T)\setminusσ_{T_W}(T)=π_{00}(T)$$ and a commuting pair of paranormal operators satisfy Weyl's theorem-II, that is $$σ_T(T)\setminusω(T)=π_{00}(T),$$ where $σ_T(T),\, σ_{T_W}(T),\,ω(T)$ and $π_{00}(T)$ are the Taylor spectrum, the Taylor Weyl spectrum, the joint Weyl spectrum and the set consisting of isolated eigenvalues of $T$ with finite multiplicity, respectively. Moreover, we prove that Weyl's theorem-II holds for $f(T)$, where $T$ is a commuting pair of paranormal operators and $f$ is an analytic function in a neighbourhood of $σ_T(T)$.
