Mathematical Sciences: Quasitriangularity in von Neumann Algebras and Other Topics

这个项目是发展一个准三角理论 半有限von Neumann代数的子代数 一些 将研究的问题是：元素的特征， 拟三角代数，邻近性问题，局部性， 有限宽度CSL代数的应用，外部嵌套，和 B（H）中的超自反性问题。 与插值的连接 理论，谐波分析和控制理论将追求。 的 提出的方法包括联合算子范数/希尔伯特-施密特范数 近似和密度参数。 这个项目的一般数学领域有其基础 希尔伯特空间算子的代数理论。 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。 这些看似 抽象对象具有令人惊讶的多种应用。 为 例如，它们在纽结理论中起着关键作用，而纽结理论又是 目前被用来研究DNA的结构。

The project is to develop a theory of quasitriangular subalgebras of semifinite von Neumann algebras. Some of the problems that will be studied are: characterizations of elements in a quasitriangular algebra, proximinality questions, locality, applications of finite width CSL algebras, external nests, and hyperreflexivity questions in B(H). Connection with interpolation theory, harmonic analysis and control theory will be pursued. The proposed methods include joint operator norm/Hilbert-Schmidt norm approximations, and density arguments. 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.