Mathematical Sciences: Research on Operators in Hilbert Space

Fialkow将继续他关于Hilbert空间上有界线性算子系统的几个问题的研究。这些问题涉及以下主题：联合次反常及矩理论中的相关问题；初等算子的谱理论；C*-代数中的多数化、因子分解和可逆因子定理。研究的一部分将关注亚正规、k-次正规和弱k-次正规算子的结构模型，重点是单边加权位移；本研究也将涉及多维功率矩问题。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。

Fialkow will continue his study of several problems concerning systems of bounded linear operators on Hilbert space. These problems concern the following topics: joint hyponormality and related problems in the theory of moments; spectral theory of elementary operators; and majorization, factorization and invertible factor theorems in C*-algebras. One part of the research will concern structural models for subnormal, k- hyponormal, and weakly k-hyponormal operators, with an emphasis on unilateral weighted shifts; this study will also concern multidimensional power moment problems. 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.