Problems in Operator Theory

University Of New Mexico, Albuquerque NM

Investigators

Abstract

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.