论文标题
紧凑型操作员在希尔伯特空间上的定量光谱扰动理论
Quantitative spectral perturbation theory for compact operators on a Hilbert space
论文作者
论文摘要
我们通过将所有操作员分组为一定速度衰减的所有操作员来介绍Hilbert太空运营商的紧凑性类别，并为属于特定紧凑型类别的运算符的分辨率的规范建立上限。结果，我们可以根据操作员规范在两个操作员的距离方面获得两个操作员的光谱距离的距离频谱的距离。
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging to a particular compactness class. As a consequence we obtain explicitly computable upper bounds for the Hausdorff distance of the spectra of two operators belonging to the same compactness class in terms of the distance of the two operators in operator norm.
