拓扑一致下降、拟Fredholm性和源于半B-Fredholm理论的算子
Toplogical uniform descent, quasi-Fredholmness and operators originated from semi-B-Fredholm theory
摘要：
本文研究了源于半B-Fredholm理论的算子，得到了关于其谱的边界和连通壳的一些结果。特别地，我们证明了作用在Banach空间上的具有拓扑一致下降的有界线性算子$T$是{ \bf BR}算子当且仅当$0$不是相关谱$σ_{\bf R}(T)=\{λ\in\CC:T-λI\notin {\bf R}\}$的聚点，其中${\bf R}$表示以下任何一类：上半Weyl算子，Weyl算子，上半Fredholm算子，Fredholm算子，具有有限（本质）下降的算子和${\bf BR}$，与${\bf R}$相关的B-正则性，如\cite{P8}。在$T,$的拟Fredholmness的较强假设下，我们得到了$T$是更大集合族${\bf R}.$的{ $\bf BR$ }算子的类似刻画
英文摘要：
In this paper we study operators originated from semi-B-Fredholm theory and as a consequence we get some results regarding boundaries and connected hulls of the corresponding spectra. In particular, we prove that a bounded linear operator $T$ acting on a Banach space, having topological uniform descent, is a {\bf BR} operator if and only if $0$ is not an accumulation point of the associated spectrum $σ_{\bf R}(T)=\{λ\in\CC:T-λI\notin {\bf R}\}$, where ${\bf R}$ denote any of the following classes: upper semi-Weyl operators, Weyl operators, upper semi-Fredholm operators, Fredholm operators, operators with finite (essential) descent and ${\bf BR}$ the B-regularity associated to ${\bf R}$ as in \cite{P8}. Under the stronger hypothesis of quasi-Fredholmness of $T,$ we obtain a similar characterization for $T$ being a {$\bf BR$} operator for much larger families of sets ${\bf R}.$
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