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Permanent link (DOI): https://doi.org/10.7939/R3FB4WV4R

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On a Generalization of the Gelfand Transform to Non-Commutative Banach Algebras Open Access

Descriptions

Other title
Subject/Keyword
Banach Algebras
Gelfand transform
Operator theory
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Guzman, Ivan E
Supervisor and department
Runde, Volker (Mathematical and Statistical Sciences)
Examining committee member and department
Bowman, John (Mathematical and Statistical Sciences)
Berger, Arno (Mathematical and Statistical Sciences)
Runde, Volker (Mathematical and Statistical Sciences)
Yaskin, Vladyslav (Mathematical and Statistical Sciences)
Lau, Anthony (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2013-09-30T13:38:11Z
Graduation date
2013-11
Degree
Master of Science
Degree level
Master's
Abstract
A Gelfand theory for an arbitrary Banach algebra A is a pair (G;A), such that: A is a C*-algebra and G : A ! A is an algebra homomorphism; G induces a bijection between the set of maximal modular left ideals of A and the set of maximal modular left ideals of A; and for every maximal modular left ideal L of A, the map GL : A=G1(L) ! A=L induced by G has dense range. We prove that if A is a postliminal C*-algebra with Gelfand theory (G;A), then no proper C*-subalgebra of A contains GA. We also show that if J is an ideal of a Banach algebra A such that A=J and J both have Gelfand theories, then A also has a Gelfand theory if we impose some conditions on J and on its Gelfand theory.
Language
English
DOI
doi:10.7939/R3FB4WV4R
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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