Date of Degree
PhD (Doctor of Philosophy)
Paul S. Muhly
If b is an inner function and T is the unit circle, then composition with b induces an endomorphism, β, of L1(T) that leaves H1(T) invariant. In this document we investigate the structure of the endomorphisms of B(L2(T)) and B(H2(T)) that implement by studying the representations of L1(T) and H1(T) in terms of multiplication operators on
B(L2(T)) and B(H2(T)). Our analysis, which was inspired by the work of R. Rochberg and J. McDonald, will range from the theory of composition operators
on spaces of analytic functions to recent work on Cuntz families of isometries and
Copyright 2010 Samuel William Schmidt
Schmidt, Samuel William. "Endomorphisms, composition operators and Cuntz families." dissertation, University of Iowa, 2010.