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.
