谱为有限个孤立本征值的算子

本文给出了谱为有限个本征值的算子其非零本征值为有限秩极点的一个充要条件.证明了这类算子是幂零算子对有限秩算子的扰动并讨论了该算子的谱同有限秩算子的谱之间的关系,最后在Hilbert空间中给出了这类算子的一个例子并讨论了广义幂零算子对紧算子的扰动.

Operators with Spectrum Consisting of Finite Isolated Eigenvalues

A necessary and sufficient condition for the operators with spectrum consisting of finite eigenvalues which are poles of finite rank except for zero is established in this paper. It is proved that this class of operators is the perturbation of finite rank operators by nilpotent operators and the relations of the spectrum between this class of operators and the correspon-ding finite rank operators is discussed. At last, an example for this class of operators is given in Hilbert Space. Furthermore, the perturbation of compact operators by quasi-nilpotent operators is discussed.