Mathematical Sciences: Nonselfadjoint Limit Algebras

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9401456 Baker The project involves the classification of triangular UHF algebras. The goal is to establish a Banach algebra classification theory for these algebras. It is further proposed to develop a classification scheme for triangular UHF K algebras. Investigations will also be made of triangular UHF algebras over the p-adics. Other investigations will be made in the areas of canonical subalgebras of AF C*-algebras, the representation theory of standard triangular UHF operator algebras, and the calculation of the first K group of certain subdiagonal subalgebras of type II von Neumann algebras. The general area of this project is operator algebras. 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. Among other problems, Professor Baker will try to classify operator algebras that can be approximated by operator algebras consisting of finite matrices. ***