Mathematical Sciences: Operators on Hilbert Space

Pearcy将研究与压缩相关的各种算子的结构理论，包括多项式有界算子、幂有界算子、弱中心算子、次正规算子和交换压缩对。在过去的12年里，Pearcy在希尔伯特空间上由一个或几个固定有界线性算子生成的对偶代数的概念上所发展的技术和结果将被使用。算符理论是研究矩阵的无限维推广的数学部分。特别地，当限制在有限维子空间中时，算子具有通常的线性性质，因此可以用矩阵表示。算子理论的中心问题是对满足附加条件的算子进行分类，这些附加条件是根据相关算子（如伴随算子）或根据基础空间给出的。算子理论是许多数学的基础，也是数学在其他科学中的许多应用的基础。

Pearcy will investigate the structure theory of various classes of operators that are related to contractions, including the polynomially bounded operators, power bounded operators, weakly centered operators, hyponormal operators, and pairs of commuting contractions. Techniques and results developed by Pearcy during the last 12 years involving the concept of dual algebra generated by one or several fixed bounded linear operators on Hilbert space will be used. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.