Mathematical Sciences: Projects in Modern Analysis

数学科学：现代分析项目

• 批准号: 8801329
• 负责人: Paul Muhly
• 金额: $ 39.83万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801329&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Projects; Modern; Analysis

The four investigators will pursue a variety of problems having to do with operators and algebras of operators on Hilbert space. One area of research is multiparameter operator theory, in which such notions as spectrum are considered in joint fashion for tuples of operators rather than for single operators. Another line of investigation concerns differentiable structure on operator algebras, including the study of unbounded derivations and of Lie group actions. Recently discovered connections between knot theory and the theory of operator algebras will be explored. The setting of Hilbert space and the linear operators that transform it is fundamental for representing many of the structures and phenomena encountered in mathematics. Basic features of this setting are infinite-dimensionality, in other words infinitely many degrees of freedom, and noncommutativity, in other words the result of a sequence of operations depends on the order in which the operations are performed. The overall aim of the research in this project is to extend still further the powerful strategy of representing things by operators.

这四位研究者将研究各种各样与希尔伯特空间上的算子和算子代数有关的问题。一个研究领域是多参数算子理论，其中诸如频谱之类的概念以联合方式考虑算子元组而不是单个算子。另一个研究方向涉及算子代数上的可微结构，包括无界推导和李群作用的研究。将探讨最近发现的结理论与算子代数理论之间的联系。希尔伯特空间的设置和变换它的线性算子是表示数学中遇到的许多结构和现象的基础。这种设置的基本特征是无限维，换句话说，无限多个自由度，和非交换性，换句话说，一系列操作的结果取决于操作执行的顺序。本项目研究的总体目标是进一步扩展用算子表示事物的强大策略。