Mathematical Sciences: Quasitriangularity in von Neumann Algebras and Other Topics

数学科学：冯·诺依曼代数和其他主题中的拟三角性

• 批准号: 9123249
• 负责人: Gary Weiss
• 金额: --
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123249&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quasitriangularity; von; Neumann

The project is to develop a theory of quasitriangular subalgebras of semifinite von Neumann algebras. Some of the problems that will be studied are: characterizations of elements in a quasitriangular algebra, proximinality questions, locality, applications of finite width CSL algebras, external nests, and hyperreflexivity questions in B(H). Connection with interpolation theory, harmonic analysis and control theory will be pursued. The proposed methods include joint operator norm/Hilbert-Schmidt norm approximations, and density arguments. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA.

该项目旨在发展半有限冯诺依曼代数的拟三角子代数理论。 将研究的一些问题包括：拟三角代数中元素的表征、邻近性问题、局部性、有限宽度 CSL 代数的应用、外部嵌套以及 B(H) 中的超自反性问题。 将寻求与插值理论、谐波分析和控制理论的联系。 所提出的方法包括联合算子范数/希尔伯特-施密特范数近似和密度参数。 该项目的一般数学领域以希尔伯特空间算子代数理论为基础。 运算符可以被认为是复数的有限或无限矩阵。 特殊类型的运算符通常放在代数中，自然称为运算符代数。 这些看似抽象的物体有着令人惊讶的多种应用。 例如，它们在结理论中发挥着关键作用，而结理论目前正被用来研究 DNA 的结构。