Pearcy will investigate the structure theory of various classes of operators that are related to contractions, including the polynomially bounded operators, power bounded operators, weakly centered operators, hyponormal operators, and pairs of commuting contractions. Techniques and results developed by Pearcy during the last 12 years involving the concept of dual algebra generated by one or several fixed bounded linear operators on Hilbert space will be used. 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.
