Eigenvalues of compactly perturbed operators in Banach spaces

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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.