Date of Award

Summer 2019

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Donald Hadwin

Second Advisor

Rita Hibschweiler

Third Advisor

Junhao Shen


This dissertation has two parts. The first part deals with Don Hadwin’s non-commutative continuous functions of countably many variables and shows that every separable C^∗-algebra can be described in terms of countably many generators x_1, x_2, ... and a single relation \varphi’(x_1, x_2, ...) = 0 where \varphi is a non-commutative continuous function. The second involves representation of operator algebras on spaces of Banach space valued measurable functions and groups of measure preserving transformations. The main emphasis concerns describing asymptotic norms based on symmetric gauge norms on L^\infty[0,1]