Operator Theory on Univariate Analytic Function Spaces

Abstract

The goal of this thesis is to study certain aspects of Toeplitz, Hankel, and composition operators, as well as the associated operator algebras, on various Hardy and Bergman spaces of univariate analytic functions. The work belongs to the general area of function theoretic operator theory, with added flavors of uniform function algebras and C*-algebras. It is hoped that the results obtained reveal new and perhaps interesting connections between properties of the symbol functions and those of the induced operators. It is also hoped that some of the methods and techniques developed in this research could help solve other problems in the theory of Toeplitz and Hankel operators beyond the scope of this thesis.