Mathematical Sciences: Projects in Operator Algebra

数学科学：算子代数项目

• 批准号: 9401174
• 负责人: Paul Muhly
• 金额: $ 9.6万
• 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: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401174&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Projects; Operator; Algebra

9401174 Muhly Muhly will investigate a range of problems in the structure theory of operator algebras. He will concentrate on the question of how the collection of Hilbert space representations of an operator algebra (or the category of Hilbert modules over the algebra) reflect on the algebra. He will study, too, the structure of operator spaces that are modules over operatoralgebras. Operators can be viewed as infinite dimensional versions of matrices. operators have a natural addition and multiplication and a collection of operators can be consider as a mathematical structure referred to as an operator algebra. These operator algebras can be represented in various explicit manners and Muhly will look at how the various representations reflect on the algebra. He will also study applications of operator algebras to questions of design and control theory. Particular attention will be given to applications to neural networks and to non-stationary control theory that occurs in materials production and noise abatement. ***

9401174 Muhly Muhly 将​​研究算子代数结构理论中的一系列问题。他将集中讨论算子代数的希尔伯特空间表示的集合（或代数上希尔伯特模的范畴）如何反映代数的问题。他还将研究算子空间的结构，算子空间是算子代数上的模块。 运算符可以被视为矩阵的无限维版本。运算符具有自然的加法和乘法，并且运算符的集合可以被视为称为运算符代数的数学结构。这些算子代数可以用各种显式方式表示，Muhly 将​​研究各种表示如何反映在代数上。他还将研究算子代数在设计和控制理论问题中的应用。将特别关注神经网络的应用以及材料生产和噪声抑制中发生的非平稳控制理论。 ***