Mathematical Sciences: Nonselfadjoint Operator Algebras

彼得斯：这个项目涉及到几个涉及非自伴随算子代数结构的问题。这些包括有限维算子代数的直接极限。一个主要的工具是解析代数的cones谱或解析范围。某些巢代数的同构类可以用有限算法确定。提出了改进和实现该算法的方法。在另一个方向上，将研究拓扑零性的概念。这个概念最近被研究用于巴拿赫代数，在算子代数的背景下，如非自伴随交叉积。非自伴算子代数是量子物理学家用来研究粒子理论的物体的三角子代数。这类代数的性质及其与动力系统的联系是我们打算研究的问题。在某些情况下，存在可计算算法。这个项目的目标是促进对基本数学结构的理论理解。＊＊＊

9504359 Peters This project involves work on several problems involving the structure of nonselfadjoint operator algebras. These include direct limits of finite dimensional operator algebras. One of the principal tools is the Connes spectrum or analytic range for analytic algebras. The isomorphism class of certain nest algebras can be determined by a finite algorithm. It is proposed to improve and implement this algorithm. In another direction an investigation will be made of the notion of topologocal nilpotence. This concept has been recently studied for Banach algebras, in the context of operator algebras, such as nonselfadjoint crossed products. Nonselfadjoint operator algebras arise as triangular subalgebras of objects used by quantum physicists to study particle theory. The properties of such algebras and their connections with dynamical systems are questions we intend to investigate. In some cases there are computable algorithms. The goal of this project is to contribute to the theoretical understanding of basic mathematical structures. ***