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. ***
