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Endomorphisms, composition operators and Cuntz families

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.

Identiferoai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-1782
Date01 May 2010
CreatorsSchmidt, Samuel William
ContributorsMuhly, Paul S.
PublisherUniversity of Iowa
Source SetsUniversity of Iowa
LanguageEnglish
Detected LanguageEnglish
Typedissertation
Formatapplication/pdf
SourceTheses and Dissertations
RightsCopyright 2010 Samuel William Schmidt

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