Topics in Function Theoretic Operator Theory

Conway教授将研究次正规算子理论和多变量算子理论中的几个主题。其中一些问题与J.E. Thomson最近的突破有关，该突破表明在有趣的情况下存在有界点评估。另一个问题涉及到为次正规n元组的算子找到一个泛函演算。本研究涉及到希尔伯特空间算子理论。这些算子本质上是复数的无限矩阵。这些对象在应用科学和纯数学的各个领域都有应用。这种类型的研究试图对这些操作符的某些重要类别进行分类。

Professor Conway will investigate several topics in the theory of subnormal operators and in several variable operator theory. Some of these questions are related to the recent breakthrough of J.E. Thomson showing that bounded point evaluations exist in interesting cases. Another question involves finding a functional calculus for subnormal n-tuples of operators. This research involves the theory of Hilbert space operators. These operators are essentially infinite matrices of complex numbers. Such objects have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important classes of these operators.