DOI

10.17077/etd.6pfob915

Document Type

Dissertation

Date of Degree

Spring 2010

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Muhly, Paul S.

First Committee Member

Muhly, Paul S.

Second Committee Member

Curto, Raul

Third Committee Member

Baker, Richard

Fourth Committee Member

Camillo, Victor

Fifth Committee Member

Meurice, Yannick

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.

Keywords

Algebra, Analysis, Composition, Cuntz, Endomorphism, Operator

Pages

iii, 51 pages

Bibliography

Includes bibliographical references (pages 50-51).

Copyright

Copyright 2010 Samuel William Schmidt

Included in

Mathematics Commons

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