Mathematical Sciences: Multivariable Operator Theory

Curto的研究将涉及多变量算子理论课题中的五个项目。这些项目包括：1。莱因哈特域和矩阵莱因哈特域上泛函希尔伯特空间上乘法谱图的描述。2.多项式次非正常算子的进一步刻画。3.利用次变态算子技术刻画矩序列的初始段。4.搜索一个Sz。几个变量下的Nagy-Foias膨胀理论。5.了解泰勒光谱和其他使用拓扑和k理论不变量的光谱系统之间的关系。希尔伯特空间算子是矩阵的无限推广。向量的无限泛化通常是一个函数，因此希尔伯特空间算子通常被建模为函数空间上的乘法算子。这个项目包括为操作符或操作符元组寻找这样的模型。一旦获得了这样的模型，关于这些算子结构的许多基本问题就变得更加自然了。＊＊＊

9401455 Curto The research of Curto will involve five projects from the subject of multivariable operator theory. These projects are the following: 1.A description of the spectral picture of multiplication on functional Hilbert spaces over Reinhardt and matrix Reinhardt domains. 2.Further characterizations of polynomial hyponormal operators. 3.Using hyponormal operator techniques to characterize initial segments of moment sequences. 4.A search for an Sz. Nagy-Foias dilation theory in several variables. 5.Understand the relationship between Taylor spectrum and other spectral systems using topological and K-theoretic invariants. Hilbert space operators are infinite generalizations of matrices. The infinite generalization of a vector is frequently a function and for this reason Hilbert space operators are frequently modeled as the operator of multiplication on a space of functions. This project involves finding such models for operators or tuples of operators. Once such models are obtained many basic questions about the structure of these operators become more natural. ***