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Ideal perturbation of elements in C*-algebras
Dissertation (MSc (Mathematics and Applied Mathematics))--University of Pretoria, 2004.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613623254253568 |
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| access_status_str | Open Access |
| author2 | Stroh, Anton |
| author_browse | Stroh, Anton |
| author_facet | Stroh, Anton |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Dissertation (MSc (Mathematics and Applied Mathematics))--University of Pretoria, 2004. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/23751 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:39:05.410Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/23751 Ideal perturbation of elements in C*-algebras Stroh, Anton upetd@ais.up.ac.za Lee, Wha-Suck No key words available UCTD Dissertation (MSc (Mathematics and Applied Mathematics))--University of Pretoria, 2004. The 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. Mathematics and Applied Mathematics unrestricted 2013-09-06T15:51:24Z 2005-01-18 2013-09-06T15:51:24Z 2005-06-14 2004 2005-01-18 Dissertation Lee, W 2004, Ideal perturbation of elements in C*-algebras, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/23751 > http://hdl.handle.net/2263/23751 http://upetd.up.ac.za/thesis/available/etd-01182005-113356/ © 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. application/pdf University of Pretoria |
| spellingShingle | No key words available UCTD Ideal perturbation of elements in C*-algebras |
| title | Ideal perturbation of elements in C*-algebras |
| title_full | Ideal perturbation of elements in C*-algebras |
| title_fullStr | Ideal perturbation of elements in C*-algebras |
| title_full_unstemmed | Ideal perturbation of elements in C*-algebras |
| title_short | Ideal perturbation of elements in C*-algebras |
| title_sort | ideal perturbation of elements in c algebras |
| topic | No key words available UCTD |
| url | http://hdl.handle.net/2263/23751 http://upetd.up.ac.za/thesis/available/etd-01182005-113356/ |