The project is to develop a theory of quasitriangular subalgebras of semifinite von Neumann algebras. Some of the problems that will be studied are: characterizations of elements in a quasitriangular algebra, proximinality questions, locality, applications of finite width CSL algebras, external nests, and hyperreflexivity questions in B(H). Connection with interpolation theory, harmonic analysis and control theory will be pursued. The proposed methods include joint operator norm/Hilbert-Schmidt norm approximations, and density arguments. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. 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. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA.
