Mathematical Sciences: Operators on Hillbert Space

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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.