Mathematical Sciences: Operators on Hillbert Space

9623197李，W-S这个项目的目的是更好地理解作用在复杂的、可分的无限维希尔伯特空间上的有界线性算子的结构。在过去的十六年里，对偶代数理论为我们提供了大量的关于压缩算子的膨胀理论、不变子空间问题和自反性问题的知识。首席研究员计划继续这一计划，现在重点研究更一般的算子类和由多个算子生成的对偶代数。同时，首席研究员还将通过交换提升定理继续她对控制理论的研究。此外，她还将继续学习C-0算子类。我目前的工作是研究算子理论，特别是研究Hilbert空间上的线性算子的结构。这些算子出现在许多数学模型中，这些数学模型广泛应用于物理、经济、工程等领域。因此，更好地了解这些运算符是至关重要的，因为它应该导致改进这些模型以及它们所做的模拟和预测的质量。

9623197 LI, W-S The purpose of this project is to obtain a better understanding of the structure of bounded linear operators acting on a complex, separable, infinite dimensional Hilbert space. During the past sixteen years, the theory of dual algebras has provided us considerable knowledge for the dilation theory of contraction operators, the invariant subspace problem, and the reflexivity problem. The principal investigator plans to continue this program, focusing now on more general classes of operators and dual algebras generated by more than one operator. At the same time, the principal investigator will also continue her research on control theory via the commutant lifting theorem. In addition, she will also continue her study of the class of C-0 operators. My current work is in operator theory, in particular studying the structure of linear operators on Hilbert spaces. These operators appear in many mathematical models, which are used in physics, economy, engineering, etc.. Therefore, a better understanding of these operators is of fundamental importance since it should lead in improving these models as well as the qualities of the simulations and forecasts made out them.