Certain C*-Algebras of Toeplitz Operators and Singular Integral Operators

本文将研究由Toeplitz算子和与维内流相关的奇异积分算子生成的C*-代数的结构。这类C*代数包括许多经典的例子。研究的重点是n大于1的情况。在这种情况下，每个代数都包含一系列需要仔细分析的理想。这些理想将用于计算K-群，K-群是C*-代数分类的重要不变量。k群也将用于研究Toeplitz算子系统的可逆性。在这方面，我们将尝试确定某些换向子理想的稳定秩。分析了单位圆上由圆的同胚导出的Toeplitz代数的若干自同构。本课题研究由奇异积分方程的经典算子生成的代数。这些方程可以追溯到工程和制造中的应用，如翼型方程和金属板的冲压。这里的抽象问题是使用不变量对这些代数进行分类。这些贡献将涉及纯数学的许多领域，包括遍历理论、分析和几何。* * *

9400600 Xia The investigation will examine the structure of C*-algebras generated by Toeplitz operators and singular integral operators associated within-dimensional flows. This class of C*-algebras includes many classical examples. The investigation is particularly directed to the case where n is greater than 1. In this case each algebra contains a chain of ideals that will be analyzed carefully. These ideals will be used to compute K- groups, which are important invariants for the classification of C*-algebras. The k-groups will also be used to study the invertibility of systems of Toeplitz operators. In this connection an attempt will be made to determine the stable rank of certain commutator ideals. An analysis will be made of certain automorphisms of the Toeplitz algebra on the unit circle which are induced by homeomorphisms of the circle. This project investigates certain algebras generated by classical operators that arise from the study of singular integral equations. These equations can be traced back to applications in engineering and manufacturing such as the equation of the airfoil and the stamping of metal plates. The abstract problem here is the classification of these algebras using invariants. The contributions will be to many fields of pure mathematics including ergodic theory, analysis and geometry. ***