Mathematical Sciences: Banach Spaces and Operator Theory

数学科学：Banach 空间和算子理论

• 批准号: 9304227
• 负责人: Alvaro Arias
• 金额: $ 7.59万
• 依托单位: University of Texas at San Antonio
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1997-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304227&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Banach; Spaces; Operator

Arias will investigate several problems in Banach space theory with applications to operator theory and probability. The main areas of research will be the local theory of Banach spaces, nest algebras for a Banach space perspective, and finite- dimensional operator theory. 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.

阿里亚斯将研究几个问题在Banach空间 理论与应用算子理论和概率。 的 主要研究领域将是Banach空间的局部理论， 一个Banach空间的观点，和有限的套代数- 维算子理论 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。