Mathematical Sciences: Unconditional Structure in Banach Spaces

数学科学：Banach 空间中的无条件结构

• 批准号: 9500125
• 负责人: Nigel Kalton
• 金额: $ 14.45万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-01 至 1999-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500125&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Unconditional; Structure; Banach

Kalton 9500125 The principal investigator plans to study a number of fundamental questions in the theory of unconditional structure in Banach spaces. Among the questions to be considered is the longstanding problem of whether a complemented subspace of a Banach space with an unconditional basis also has an unconditional basis, and a similar problem for complemented subspaces of Banach lattices. The resolution of these problems could have a profound effect on the theory of Banach spaces. Another question to be studied is whether a Banach space in which every closed subpsace has an unconditional basis (or just local unconditional structure) is necessarily a Hilbert space. A number of other problems concerning unconditional structure are also to be investigated. Unconditional bases are a natural framework for the study of the decomposition of functions (or signals) into basis elements (or simpler pure components) as in the modern theory of wavelets. This proposal is concerned with studying situations where such decompositions exist and where they fail to exist. By studying the possible unconditional bases of a certain space or class of functions one is able to obtain important information concerning the space. ***

Kalton 9500125主要研究人员计划研究Banach空间中无条件结构理论中的许多基本问题。 在要考虑的问题中，有一个长期存在的问题是，与无条件的基础的Banach空间的补充子空间是否也有无条件的基础，并且对于Banach Lattices的补充子空间也是一个类似的问题。 解决这些问题的解决可能会对Banach空间的理论产生深远的影响。 要研究的另一个问题是，每个封闭的子盖子都有无条件基础（或只是局部无条件结构）的Banach空间是否必然是希尔伯特的空间。 还将研究有关无条件结构的许多其他问题。 无条件基础是研究函数（或信号）分解为基础元素（或更简单的纯组件）的自然框架，如现代小波的理论。 该提案与研究存在这种分解以及它们不存在的情况有关。 通过研究某个空间或一类功能类别的无条件基础，人们就可以获得有关该空间的重要信息。 ***