Problems in Operator Theory

随着世界物理模型的改进以及其他科学和技术的进步，对算符的分析和不可对易的固有现象一直在发展。这个项目致力于研究数学物理、非对易分析和几何以及单变量和多变量算子函数理论中出现的算子理论中的公开问题。该项目还旨在加强几个数学领域之间的联系，促进通识教育，并加强学生的研究。拟议的主题包括建立具有类似于相应标量函数的经典性质的非对易变元的算子函数的性质，了解扰动对算子谱子空间的影响，以及研究属于算子代数的元素的结构。这项拟议研究的实质在于开发创新的方法来处理出现在问题中的非对易的不同影响，以及其他方面。这样的方法预计将出现在分析和算符理论的各种技术的微妙综合中。

Analysis of operators and inherent phenomena of noncommutativity have been developing in response to refinement of physical models of the world as well as to advancement of other sciences and technology. This project is devoted to open problems in operator theory that arise in mathematical physics, noncommutative analysis and geometry, and the theory of single-variable and multivariate operator functions. The project is also designed to strengthen connections between several areas of mathematics, contribute to general education, and enhance student research.The proposed topics include establishing properties of operator functions with noncommuting arguments that are similar to classical properties of the respective scalar functions, understanding the impact of perturbations on spectral subspaces of operators, and studying the structure of elements belonging to operator algebras. The essence of the proposed research consists in developing innovative methods for handling different effects of noncommutativity that appear in the problems, and beyond. Such methods are expected to emerge from subtle synthesis of various techniques in analysis and operator theory.