Mathematical Sciences: Banach Spaces, Operators and Related Topics

数学科学：Banach 空间、运算符及相关主题

• 批准号: 9007889
• 负责人: Stanislaw Szarek
• 金额: $ 13.48万
• 依托单位: Case Western Reserve University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007889&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Banach; Spaces; Operators

Professor Szarek will study the isomorphic theory of Banach spaces, some problems from finite dimensional operator theory, and scientific computation linked to these areas. One of the problems to be investigated is whether extremely rigid infinite dimensional Banach spaces exist where for example the Calkin algebra is abelian or consists only of multiples of the identity operator. 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 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.

Szarek教授将研究巴拿赫的同构理论 空间，有限维算子理论的一些问题， 和科学计算联系在一起。 之一 要研究的问题是， 维Banach空间存在，例如Calkin 代数是阿贝尔的或只由单位元的倍数组成 操作符. 该奖项将支持巴拿赫几何的研究 空间. 在有限维中，所有向量空间本质上都是 一样的 但是在无限维的情况下 在这里，情况远非如此。 Banach空间是无限的 引入了附加结构的维空间， 空间中点与点之间距离的不同概念。 等 空间在数学中有着广泛的应用， 应用。