Ideal perturbation of elements in C*-algebras

dc.contributor.advisorStroh, Antonen
dc.contributor.emailupetd@ais.up.ac.zaen
dc.contributor.postgraduateLee, Wha-Sucken
dc.date.accessioned2013-09-06T15:51:24Z
dc.date.available2005-01-18en
dc.date.available2013-09-06T15:51:24Z
dc.date.created2005-06-14en
dc.date.issued2004en
dc.date.submitted2005-01-18en
dc.descriptionDissertation (MSc (Mathematics and Applied Mathematics))--University of Pretoria, 2004.en
dc.description.abstractThe aim of this thesis is to prove the lifting property of zero divisors, n-zero divisors, nilpotent elements and a criteria for the lifting of polynomially ideal elements in C*-algebras. Chapter 1 establishes the foundation on which the machinery to prove the lifting properties stated above rests upon. Chapter 2 proves the lifting of zero divisors in C*-algebras. The generalization of this problem to lifting n-zero divisors in C*-algebras requires the advent of the corona C*-algebra, a result of the school of non-commutative topology. The actual proof reduces the general case to the case of the corona of a non-unital _-unital C*-algebra. Chapter 3 proves the lifting of the property of a nilpotent element also by a reduction to the case of the corona of a non-unital _-unital C*-algebra. The case of the corona of a non-unital _-unital C*-algebra is proved via a lifting of a triangular form in the corona. Finally in Chapter 4, a criterion is established to determine exactly when the property of a polynomially ideal element can be lifted. It is also shown that due to topological obstructions, this is not true in any C*-algebra.en
dc.description.availabilityunrestricteden
dc.description.departmentMathematics and Applied Mathematicsen
dc.identifier.citationLee, W 2004, Ideal perturbation of elements in C*-algebras, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/23751 >en
dc.identifier.upetdurlhttp://upetd.up.ac.za/thesis/available/etd-01182005-113356/en
dc.identifier.urihttp://hdl.handle.net/2263/23751
dc.language.isoen
dc.publisherUniversity of Pretoriaen_ZA
dc.rights© 2005, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.en
dc.subjectNo key words availableen
dc.subjectUCTDen_US
dc.titleIdeal perturbation of elements in C*-algebrasen
dc.typeDissertationen

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