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; 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将研究操作员代数理论中的一系列问题。他将集中讨论一个问题的问题，即操作员代数（或代数上希尔伯特模块的类别）的收集如何反思代数。他也将研究操作员空间的结构，即操作员的模块。 可以将操作员视为矩阵的无限尺寸版本。操作员具有自然的添加和乘法，并且可以将运算符的集合视为一种数学结构，称为操作员代数。这些运算符代数可以用各种明确的举止表示，Muhly将研究各种表示形式如何反映代数。他还将研究操作员代数对设计和控制理论问题的应用。特别关注对材料生产和消除噪声中发生的神经网络和非平稳控制理论的应用。 ***