Date of Degree
2010
Document Type
dissertation
Degree Name
PhD (Doctor of Philosophy)
Department
Mathematics
First Advisor
Paul S. Muhly
Abstract
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
Hilbert C*-modules.
Pages
iii, 51
Bibliography
50-51
Copyright
Copyright 2010 Samuel William Schmidt
Recommended Citation
Schmidt, Samuel William. "Endomorphisms, composition operators and Cuntz families." dissertation, University of Iowa, 2010.
http://ir.uiowa.edu/etd/597.