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.
| Identifer | oai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-1782 |
| Date | 01 May 2010 |
| Creators | Schmidt, Samuel William |
| Contributors | Muhly, Paul S. |
| Publisher | University of Iowa |
| Source Sets | University of Iowa |
| Language | English |
| Detected Language | English |
| Type | dissertation |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | Copyright 2010 Samuel William Schmidt |
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