Mathematical Sciences: Operator Spaces and Operator Algebras

数学科学：算子空间和算子代数

• 批准号: 9302989
• 负责人: Zhong-Jin Ruan
• 金额: $ 6.14万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302989&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operator; Spaces; Algebras

Ruan will continue his investigations in operator spaces. This will include the connection with Banach spaces and the application to C*-algebras and von Neumann algebras, non-self- adjoint operator algebras, and applications of operator spaces to quantum groups. 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 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, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.

Ruan将继续在操作员空间进行调查。 这将包括与Banach空间的连接以及与C*-Algebras和Von Neumann代数，非固定伴随操作员代数以及操作员空间应用于量子组的应用。 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。 这些抽象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，而该理论又被用来研究DNA的结构，并且在非交通性几何形状中至关重要，这在物理学中变得越来越重要。