Mathematical Sciences: Nonselfadjoint Operator Algebras

小行星9504359 这个项目涉及到非自伴算子代数结构的几个问题。这些包括有限维算子代数的直接极限。其中一个主要工具是解析代数的Connes谱或解析值域。某些套代数的同构类可以通过有限算法确定。提出了对该算法的改进和实现。在另一个方向的调查将作出的概念拓扑niligocal。这个概念最近已经研究了Banach代数，在算子代数的背景下，如非自伴交叉产品。 非自伴算子代数作为 量子物理学家用来研究粒子理论的物体。性能 这种代数及其与动力系统的联系是一个问题 我们打算调查 在某些情况下，存在可计算算法。 这个项目的目标是有助于理论上的理解 基本的数学结构。 ***

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. ***