Date of Award
Doctor of Philosophy
In this dissertation we investigate spaces of analytic functions defined on the open unit disk that satisfy some natural boundry conditions. These new spaces are called Bloch type spaces. Given a positive integer m, the m-Bloch type space, denoted by B^(m), consists of all analytic functions which map from the open unit disk to the complex space with boundry conditions similar to the Bloch space using the n-th degree derivative. Following the leadership of Zygmund, Bloch and other well-known researchers, we consider closed subspaces of B^(m) by imposing natural reducing conditions. These closed subspaces provide an easier platform to derive properties which can be lifted to the main space.We prove several results relating to the aforementioned spaces, including that the various spaces are isometrically isomorphc as normed spaces. We observe that these isomorphisms allow for the transfer of some classes of operators from a lower order space to a higher order one. Examples of such spaces include the surjective isometries of the Bloch and Zygmund spaces and operators defined from them.We investigate further on how the knowledge of surjective isometries determine the form of the hermitian operators.
dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Taylor, Aaron Larmiah, "Classes of Operators on Spaces" (2016). Electronic Theses and Dissertations. 1526.