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.

阮将继续在操作员空间进行调查。 这将包括与 Banach 空间的连接以及对 C* 代数和冯诺依曼代数、非自伴算子代数的应用以及算子空间在量子群中的应用。 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。 这些抽象对象具有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于研究 DNA 的结构，并且它们在非交换几何中具有根本重要性，而非交换几何在物理学中变得越来越重要。