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.

该项目是为了发展半五次von Neumann代数的准二元亚代代代代代数理论。 将要研究的一些问题是：准代数中的元素的特征，近端问题，局部性，有限宽度CSL CSL代数，外部巢和B（h）中的超级反射性问题。 将追求与插值理论，谐波分析和控制理论的联系。 所提出的方法包括联合操作员规范/Hilbert-Schmidt Norm近似值和密度参数。 该项目数学的一般领域在希尔伯特太空运营商代数理论中具有其基础。 可以将操作员视为复数的有限或无限矩阵。 特殊类型的操作员通常将其放在代数中，自然称为操作员代数。 这些看似抽象的对象具有令人惊讶的应用。 例如，它们在结理论中起着关键作用，而这反过来又被用来研究DNA的结构。