Hadwin will continue his work on approximate similarity and on closures of direct sums of classes of operators. He will also study invariant operator ranges in a von Neumann algebra, and investigate a new version of K-theory based on operator ranges. In addition, Hadwin will study operator algebras from a purely algebraic point of view. This is expected to contribute to both operator theory and abstract algebra. 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.
