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.

阮将继续他在运营商空间的调查。 这将包括与巴拿赫空间和 应用于C*-代数和冯诺依曼代数，非自 伴随算子代数，以及算子空间在 量子群 这个项目的一般数学领域有其基础 在Hilbert空间算子代数理论中。 运营商 可以被认为是复数的有限或无限矩阵 号码 特殊类型的运算符通常放在 代数，自然称为算子代数。 这些抽象 物体的应用范围之广令人惊讶。 比如说， 它们在纽结理论中起着关键作用，而纽结理论目前 被用来研究DNA的结构， 在非对易几何中的重要性， 在物理学中变得越来越重要。