Mathematical Sciences: The Structure of Banach Spaces

数学科学：Banach 空间的结构

• 批准号: 9208482
• 负责人: Haskell Rosenthal
• 金额: $ 23.01万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208482&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structure; Banach; Spaces

The proposers will study several problems concerning the structure of Banach spaces. Rosenthal and Odell will focus mainly on infinite-dimensional issues, while Mascioni will study quantitative invariants for finite-dimensional spaces. Rosenthal and Odell will work on the subspace structure of general non- reflexive spaces and of quotients of certain spaces with separable duals. Mascioni will study invariants connected with the uniform approximation property. He will investigate the order of growth of the uniformity function of Lp-spaces, and the duality-order of growth of general spaces with the uap. Banach space theory is that part of mathematics that attempts to generalize to infinitely many dimensions the structure of 3-dimensional Euclidean (i.e.ordinary) space. The axioms for the distance function in a Banach space are more relaxed than those for Euclidean distance (For example, the "parallelogram law" is not required to hold.), and as a result, the "geometry" of a Banach space can be quite exotic. Much of the research in this area concerns studying the structure theory of Banach spaces.

提案人将研究有关的几个问题， Banach空间的结构 罗森塔尔和奥德尔将集中精力 主要研究无限维问题，而马肖尼将研究 有限维空间的定量不变量。 罗森塔尔 和奥德尔将工作的子空间结构的一般非- 自反空间和某些空间的直子， 可分离的 马肖尼将研究不变量与 一致逼近性质。 他将调查 Lp-空间的一致性函数的增长阶， 一般空间增长的对偶序与uap Banach空间理论是数学的一部分， 试图将其推广到无限多个维度， 三维欧氏空间的结构。 的 Banach空间中距离函数的公理更多 比欧几里得距离的那些更宽松（例如， “法律”不需要持有。），结果， 巴拿赫空间的“几何学”可以是相当奇异的。 大部分 这方面的研究涉及到结构理论的研究 Banach空间。