Fialkow will continue his study of several problems concerning systems of bounded linear operators on Hilbert space. These problems concern the following topics: joint hyponormality and related problems in the theory of moments; spectral theory of elementary operators; and majorization, factorization and invertible factor theorems in C*-algebras. One part of the research will concern structural models for subnormal, k- hyponormal, and weakly k-hyponormal operators, with an emphasis on unilateral weighted shifts; this study will also concern multidimensional power moment 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.
