Professor Fialkow will study several questions in multivariable operator theory concerning the structure of bounded linear operators in Hilbert space and the structure of certain associated C* algebras. One aspect of the research concerns the solution of systems of linear equations in C* algebras. Another facet involves polynomially bounded hyponormal weighted shifts. A final topic is the study of structural and spectral invariants for quasisimilarity of operators. The latter research is particularly concerned with characterizing those operators quasisimilar to the unilateral shift and determining their spectral properties. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. This type of research is an attempt to classify certain important categories of such objects.
