Mathematical Sciences: Structural Properties of Non-Selfadjoint Operator Algebras

点击翻译按钮获取中文摘要

9500839 Orr This proposal describes research into the structural properties of non-self-adjoint operator algebras. This is a field which combines the algebraic insights of the older field of self-adjoint operators, from which it grows, with the techniques of single operator theory. The aim in this proposal is to build on the success that recent applications of a new circle of ideas have had with important and difficult problems in the field. The last few years have seen the interplay of two ideas, "infinite multiplicity algebras" and "interpolating operators" lead to the solution of a number of longstanding problems in the field. The effect has been to open up one class of non-selfadjoint operator algebras to a whole new level of understanding. In individual work, one investigator proposes to further study and classify maximal triangular algebras, while Pitts proposes to study (and hopefully complete) the similarity theory for distributive commutative subspace lattice algebras and to classify the analytic algebras of this type. Operators can be viewed as finite of infinite matrices of complex numbers. In this way a collect of operators can often be given an algebraic structure and referred to as an operator algebra. The study of these algebras of operators is rooted in mathematical physics. The main problem in the theory of algebras is to classify these algebras so that equivalent or similar algebras can be recognized. This project deals with the classification problem for operator algebras that have elements (viewed as matrices) in triangular form. ***