Eigenvalues of compactly perturbed operators in Banach spaces

紧算子特征值的渐近行为分析是算子理论的一个经典课题，近40年来得到了广泛的研究。由于B. Carl， H. König和A. Pietsch等数学家的结果，这些特征值的行为现在已经很好地理解了。该项目关注的问题是，这些经典结果是否以及在多大程度上可以扩展到更广泛的摄动理论背景。更确切地说，我们的目的是研究那些由其他算子通过紧摄动产生的线性算子的特征值。这种扩展的观点允许许多新的应用，除了一般理论之外，本项目将研究这些应用。

The analysis of the asymptotic behavior of eigenvalues of compact operators is a classical topic of operator theory, which has been extensively studied in the last 40 years. Due to results of mathematicians such as B. Carl, H. König and A. Pietsch, the behavior of such eigenvalues is now very well understood. This project is concerned with the question if, and how far, these classical results can be extended to a wider, perturbation theoretical context. More precisely, our aim is to study the eigenvalues of those linear operators which arise from other operators by some compact perturbation. This extended point of view allows for many new applications, which, in addition to the general theory, will be studied in this project.