Mathematical Sciences: RUI: Problems in Operator Theory and Matrix Analysis

罗德曼打算研究算子论和矩阵分析中各种相互关联的问题。这些问题包括矩阵和算子值函数的内插问题，矩阵和算子的完备化问题，线性保持，扰动理论的几个方面，以及频谱分配问题。算子论是研究矩阵的无限维广义的数学部分。特别地，当被限制在有限维子空间时，算子具有通常的线性性质，因此可以用矩阵来表示。算子理论中的中心问题是根据伴随算子(例如伴随算子)或基础空间对满足附加条件的算子进行分类。算符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。

Rodman intends to study a variety of interrelated problems in operator theory and matrix analysis. These include interpolation problems for matrix and operator valued functions, completions of matrices and operators, linear preservers, several aspects of perturbation theory, and spectrum assignment 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.