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.

这四名调查人员将与希尔伯特（Hilbert）领域的运营商和代数有关的操作员和代数都有各种问题。 一个研究领域是多参数运算符理论，其中，对于操作员而不是单个操作员而言，以共同方式考虑了频谱的概念。 另一项调查涉及对操作员代数的可区分结构，包括研究无限的推导和谎言群体行为。 最近将探讨结理论与代数理论之间的联系。 希尔伯特空间的设置和转换它的线性操作员对于代表数学中遇到的许多结构和现象至关重要。 这种设置的基本特征是无限二维性，换句话说，无限的自由度和非征收性程度，换句话说，操作顺序的结果取决于执行操作的顺序。 该项目中该研究的总体目的是进一步扩展运营商代表事物的有力策略。