Eigenvalues of compactly perturbed operators in Banach spaces

Banach空间中紧扰动算子的特征值

• 批准号: 320146460
• 负责人: Dr. Marcel Hansmann
• 金额: --
• 依托单位: Professur Analysis - Peter Stollmann
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/320146460?language=en
• 关键词: Eigenvalues; compactly; perturbed; operators; Banach

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.

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，在过去的 40 年里得到了广泛的研究。由于 B. Carl、H. König 和 A. Pietsch 等数学家的研究成果，此类特征值的行为现在已得到很好的理解。该项目关注的问题是这些经典结果是否可以以及在多大程度上可以扩展到更广泛的微扰理论背景。更准确地说，我们的目标是研究那些线性算子的特征值，这些线性算子是由其他算子通过某种紧扰动产生的。这种扩展的观点允许许多新的应用，除了一般理论之外，本项目还将研究这些应用。

项目成果

Eigenvalues of compactly perturbed operators via entropy numbers

通过熵数求紧扰动算子的特征值

• DOI: 10.4171/jst/291
• 发表时间: 2020
• 期刊: Journal of Spectral Theory
• 影响因子: 1
• 作者: M. Hansmann

Some Remarks on Upper Bounds for Weierstrass Primary Factors and Their Application in Spectral Theory

关于维尔斯特拉斯主因子上界的一些评论及其在谱理论中的应用

• DOI: 10.1007/s11785-017-0695-z
• 发表时间: 2017
• 期刊: Complex Analysis and Operator Theory
• 影响因子: 0.8
• 作者: M. Hansmann