Mathematical Sciences: RUI: Structural Problems of Limit Subalgebras of AF C* -Algebras

9500566 Hudson非自伴算子代数理论，特别是近似有限C*-代数的极限子代数理论，近年来得到了迅速的发展。该研究涉及三角AF代数及其理想格的结构，三角AF代数中各种理想的根结构和分类，算子代数中的因式分解问题，三角AF代数单位球的几何，以及算子代数的代数拓扑考虑。运算符可以被视为复数的有限或无限矩阵。通过这种方式，运算符的集合通常可以被赋予一个代数结构，并被称为运算符代数。在处理其元素可以实现为无限矩阵的算子代数的情况下，重要的是理解代数是如何构造的，或者可以从有限矩阵中近似出来。近似有限算子代数是有限维子代数的极限。这一研究将有助于理解这些自然算子代数的结构。***

9500566 Hudson The theory of nonselfadjoint operator algebras, and in particular, the theory of limit subalgebras of approximately finite C*-algebras, has experienced rapid development in recent years. The proposed research concerns the structure of triangular AF algebras and their lattices of ideals, the radical structure and classification of various types of ideals in triangular AF algebras, factorization questions in operator algebras, the geometry of the unit ball of triangular AF algebras, and algebraic topology considerations within the context of operator algebras. Operators can be viewed as finite or infinite matrices of complex numbers. In this way a collection of operators can often be given an algebraic structure and referred to as an operator algebra. In the case where one is dealing with operator algebras whose elements can be realized as infinite matrices, it is important to understand how the algebra is constructed or can be approximated out of finite matrices. An approximately finite operator algebra is a limit of finite dimensional subalgebras. This research will contribute to understanding the structure of these natural operator algebras. ***