Wely定理与$(\omega)$性质的等价性

The Equivalence between Property $(\omega)$ and Weyl's Theorem

中文关键词:  Wely定理  $(\omega)$性质  谱.

英文关键词:Weyl's theorem  property $(\omega)$  spectrum.

中文摘要:

      设$T$为Hilbert空间$H$上的有界线性算子,如果对于任给$B\in B(H)$,有$TB$和$BT$同时为Fredholm算子且都与$B$有相同的指标, 或者同时不为Fredholm算子, 那么我们称$T$为一致Fredholm指标算子(简写为CFI). 在本文中, 将用CFI算子定义一个新的谱集, 利用这个谱集, 我们研究了算子T与其共轭算子T$^*$的Weyl定理和$(\omega)$性质的等价性. 之后, 算子矩阵的$(\omega)$性质也得到了研究.

英文摘要:

      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.