Mathematical Sciences: Structure of Infinite-Dimensional Banach Spaces

数学科学：无限维 Banach 空间的结构

• 批准号: 8903197
• 负责人: Haskell Rosenthal
• 金额: $ 27.09万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903197&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Infinite; Dimensional

Professors Rosenthal and Odell will work on a variety of problems in the theory of Banach spaces. One central problem concerns identifying the complemented subspaces of the space of absolutely integrable functions on an interval. This is related to the structure of Banach spaces and convex sets failing the Radon-Nikodym property. The question of the existence of subspaces isomorphic to the space of null or absolutely summable sequences in a hereditarily non-reflexive Banach space will be pursued. The approach Rosenthal and Odell will use involves analysis of the structure of spaces of Baire functions. Their recently invented notion of governance of a class of Banach spaces by a function will also play an important role. The theory of Banach spaces is about analysis in infinitely many dimensions. For each finite dimension n, there is only one n-dimensional space, in most respects as well understood in general as in the familiar cases when n is 1, 2, or 3. These are used to keep track of situations in which there are only finitely many degrees of freedom. When the number of degrees of freedom becomes infinite, as would for instance be necessary to describe the configuration of a piece of string, there are many possible reasonable choices for the ambient space in which to perform analysis. The work supported by this award is largely concerned with the ways in which these spaces fit into another, a line of investigation that lays bare a good deal of their structure.

罗森塔尔教授和奥德尔教授将研究各种 Banach空间理论中的一些问题。一个中心问题是 涉及确定空间的补子空间 区间上的绝对可积函数这是 与Banach空间和凸集的结构有关 拉东-尼科迪姆的财产的存在问题 同构于零或绝对可和空间的子空间 序列在遗传非自反Banach空间将是 追求。罗森塔尔和奥德尔将使用的方法包括 Baire函数空间的结构分析。他们的 最近发明的一类Banach空间的治理概念 空间的功能也将发挥重要作用。 Banach空间的理论是关于无限空间中的分析 多维度。对于每个有限维n，只有一个 n维空间，在大多数方面， 一般如在n为1、2或3的熟悉情况中。这些是 用来记录只有一个人的情况， 多个自由度。当自由度的数量 变成了无限的，例如， 一根绳子的配置，有许多可能 合理选择表演的环境空间 分析.该奖项所支持的工作在很大程度上受到关注 与这些空间相互融合的方式， 调查揭示了他们的大量结构。