Mathematical Sciences: Structural Properties of Non Self Adjoint Operator Algebras

Orr和Pitts将研究非自伴随算子代数的结构。特别地，他们提出了对连续巢代数中所有封闭的双面理想进行分类。理解这些理想可能会导致三角算子代数的新构造和新技术。此外，Pitts提出寻找比超自反性更弱的条件来保证CSL是稳定的，Orr提出研究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在希尔伯特空间算子的代数理论中有其基础。运算符可以被认为是有限或无限的复数矩阵。特殊类型的运算符通常放在一个代数中，自然地称为运算符代数。这些看似抽象的对象有着各种各样的应用。例如，它们在结理论中起着关键作用，而结理论目前正被用于研究DNA的结构。

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.