The metric compactification and its applications in analysis and dynamics

度量紧化及其在分析和动力学中的应用

• 批准号: 2467850
• 金额: --
• 依托单位: University of Kent
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2467850
• 关键词: metric; compactification; its; applications; analysis

The metric compactification of a metric space has been an object of study in a variety of fields most notably in geometric group theory and dynamics. In recent years some interesting applications in geometric and functional analysis have been found. However, in most settings in analysis there is only a limited amount of knowledge of the structure of the metric compactifications, as in most settings the metric spaces are not proper. One of the objectives of the project is to gain a deeper understanding of the structure of the metric compactification in a variety of important settings in analysis, such as operator algebras, e.g. B(H), and specific classes of Banach spaces. A second objective of the project is to further develop applications of the metric compactification in the dynamics of fixed point free mappings and Denjoy-Wolff type theorems and in fixed point theory. There are some open problems in this field, which are known to be hard, but of significant interest.

度量空间的度量紧化一直是许多领域的研究对象，尤其是在几何群论和动力学中。近年来，度量紧化在几何分析和泛函分析中得到了一些有趣的应用，然而，在大多数分析环境中，人们对度量紧化的结构知之甚少，因为在大多数环境中，度量空间是不恰当的。该项目的目标之一是获得更深入的了解结构的度量紧化在各种重要的设置在分析，如算子代数，如B（H），和特定类别的Banach空间。该项目的第二个目标是进一步发展度量紧化在不动点自由映射的动力学和Denjoy-Wolff型定理以及不动点理论中的应用。在这一领域有一些公开的问题，这是众所周知的困难，但重大的利益。