Mathematical Sciences: Operators on Hilbert Space

Pearcy将研究各种结构理论， 与收缩相关的运算符类，包括 多项式有界算子，幂有界算子， 弱中心算子、亚正规算子和 通勤收缩 开发的技术和成果 皮尔西在过去12年中涉及的概念， 由一个或多个固定有界线性代数生成的代数 将使用希尔伯特空间上的算子。 算子理论是数学中研究 矩阵的无穷维推广 特别是， 当限制到有限维子空间时，算子具有 通常的线性性质，因此可以表示为 矩阵 算子理论的中心问题是分类 满足附加条件的算子 关联算子（例如伴随算子）或 底层空间 算子理论是数学的基础， 以及数学在其他科学中的应用。

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.