Formalizing Categorical and Algebraic Constructions in Operator Theory

Authors

William Benjamin Grilliette, University of Nebraska-LincolnFollow

First Advisor

David R. Pitts

Date of this Version

Spring 3-31-2011

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor David R. Pitts. Lincoln, Nebraska: January, 2011

Copyright 2011 William Benjamin Grilliette

Abstract

In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*-algebra and utilization of classical algebraic tools, such as Tietze transformations.