Mathematical Sciences: Problems in Banach Spaces

数学科学：Banach 空间中的问题

• 批准号: 9001344
• 负责人: Peter Casazza
• 金额: $ 4.6万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001344&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Banach; Spaces

Professor Casazza will conduct research on several problems in the theory of Banach spaces. They involve (i) uniqueness of unconditional and symmetric structures in finite dimensional spaces, (ii) various forms of the Approximation Property, and (iii) the existence of prime Banach spaces. This award will support research in the geometry of Banach spaces. In finite dimensions, all vector spaces are essentially the same. But in the infinite dimensional situation primarily of interest here, this is far from the case. Banach spaces are infinite dimensional spaces with the additional structure introduced by varying notions of distance between points in the space. Such spaces have wide application in mathematics, both pure and applied.

Casazza教授将针对Banach空间理论中的几个问题进行研究。 它们涉及（i）有限维空间中无条件和对称结构的唯一性，（ii）各种形式的近似性质，以及（iii）素巴纳赫空间的存在。 该奖项将支持巴拿赫空间几何的研究。 在有限维中，所有向量空间本质上是相同的。 但在我们主要感兴趣的无限维度情况下，情况却远非如此。 Banach 空间是无限维空间，具有通过改变空间中点之间的距离概念引入的附加结构。 这样的空间在数学和应用数学中都有广泛的应用。