Mathematical Sciences: Structural Properties of Non Self Adjoint Operator Algebras

数学科学：非自伴随算子代数的结构性质

• 批准号: 9204811
• 负责人: John Orr
• 金额: $ 10.98万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204811&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structural; Properties; Non

Orr and Pitts will study the structure of nonselfadjoint operator algebras. In particular, they propose to classify all closed two-sided ideals in continuous nest algebras. Understanding these ideals is likely to lead to new constructions and techniques with triangular operator algebras. Additionally, Pitts proposes to find conditions weaker than hyperreflexivity which ensure that a CSL is stable, and Orr proposes to study ideal structure of CSL algebras and new maximal triangular algebras. 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.

Orr和Pitts将研究非自伴算子代数的结构。特别地，他们提出了对连续套代数中所有闭双边理想的分类。理解这些理想可能会导致三角算子代数的新的构造和技巧。此外，Pitts建议寻找比超自反更弱的条件来确保CSL是稳定的，Orr建议研究CSL代数的理想结构和新的极大三角代数。这个项目的一般数学领域以希尔伯特空间算子的代数理论为基础。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一个代数中，自然称为运算符代数。这些看似抽象的对象有着令人惊讶的各种应用。例如，它们在纽结理论中扮演着关键角色，而纽结理论目前正被用于研究DNA的结构。