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. ***

小行星9401174 Muhly将调查一系列问题的结构理论的算子代数。他将集中在如何收集的希尔伯特空间表示的算子代数（或类别的希尔伯特模块的代数）反映的问题。他还将研究算子空间的结构，即算子代数上的模。 运算符可以看作是矩阵的无限维形式。运算符具有自然加法和乘法，且运算符集合可以被认为是被称为运算符代数的数学结构。这些算子代数可以用各种明确的方式表示，Muhly将研究各种表示如何反映代数。他还将研究算子代数的应用问题的设计和控制理论。特别注意将给予神经网络和非平稳控制理论，发生在材料生产和噪音消除的应用。 ***