算子矩阵的Samuel重数与Browder谱
Samuel multiplicities and Browder Spectrum of Operator Matrices
摘要：
本文证明了X. Fang在[8]中提出的一些算子类等价于一些著名的算子类。例如，在希尔伯特空间上的类移位半弗雷德霍姆算子与上半Browder算子的概念是一致的.对于Samuel多重性的应用，我们分别描述了$\bigcap_{C\in B(K,\,H)}σ_{ab}(M_{C}),\bigcap_{C\in B(K,\,H)}σ_{sb}(M_{C})$和$\bigcap_{C\in B(K,\,H)}σ_{b}(M_{C}),$的集合，其中$M_{C}=({array}{cc}A&C 0&B {array})$表示作用于希尔伯特空间$H\oplus K$的2 × 2上三角算子矩阵。
英文摘要：
we show that the definitions of some classes of semi-Fredholm operators, which use the language of algebra and first introduced by X. Fang in [8], are equivalent to that of some well-known operator classes. For example, the concept of shift-like semi-Fredholm operator on Hilbert space coincide with that of upper semi-Browder operator. For applications of Samuel multiplicities we characterize the sets of $\bigcap_{C\in B(K,\,H)}σ_{ab}(M_{C}),\bigcap_{C\in B(K,\,H)}σ_{sb}(M_{C})$ and $\bigcap_{C\in B(K,\,H)}σ_{b}(M_{C}),$ respectively, where $M_{C}=({array}{cc}A&C 0&B {array})$ denotes a 2-by-2 upper triangular operator matrix acting on the Hilbert space $H\oplus K$.
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