Mathematical Sciences: Extending Hilbert Space Operators

阿格勒将继续他的发展，一个非常普遍的 希尔伯特空间上算子的扩张理论， 对于包括次正规算子的许多类算子， n-对称算子和m-等距算子。 这首先需要 确定与给定的 操作员，为扩展找到一个好的模型理论， 最后应用该构造证明新的定理。 在这些问题上取得进展将是许多人感兴趣的， 分析. 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。

Agler will continue his development of a very general extension theory for operators on Hilbert spaces that would apply to many classes of operators including subnormal operators, n-symmetric operators, and m-isometries. This will require first identifying the class of extensions that would go with a given operator, finding a good model theory for the extension, and finally applying the construction to prove new theorems. Progress on these problems will be of interest to many parts of analysis. 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.