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Riesz theory and Fredholm determinants in Banach algebras
Thesis (PhD (Mathematics))--University of Pretoria, 2006.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613453324124160 |
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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 | © 1999, 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 | Thesis (PhD (Mathematics))--University of Pretoria, 2006. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/30088 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:36:23.211Z |
| 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:2263/30088 Riesz theory and Fredholm determinants in Banach algebras Stroh, Anton upetd@up.ac.za Swart, Johan Bapela, Manas Majakwane Operator algebras Linear algebraic groups UCTD Thesis (PhD (Mathematics))--University of Pretoria, 2006. In the classical theory of operators on a Banach space a beautiful interplay exists between Riesz and Fredholm theory, and the theory of traces and de¬terminants for operator ideals. In this thesis we obtain a complete Riesz de¬composition theorem for Riesz elements in a semi prime Banach algebra and on the other hand extend the existing theory of traces and determinants to a more general setting of Banach algebras. In order to obtain some of these results we use the notion of finite multiplicity of spectral points to give a characterization of the essential spec¬trum for elements in a Banach algebra. As an immediate corollary we obtain the well-known characterization of Riesz elements namely that their non-zero spectral points are isolated and of finite multiplicities. In the final chapter of the thesis we use Plemelj's type formulas to define a determinant on the ideal of finite rank elements and show that it extends continuously to the ideal of nuclear elements. Mathematics and Applied Mathematics unrestricted 2013-09-07T17:54:39Z 2006-12-04 2013-09-07T17:54:39Z 1999-10-01 2006-12-04 2006-12-04 Thesis Bapela, MM 1999, Riesz theory and Fredholm determinants in Banach algebras, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/30088 > H751/ag http://hdl.handle.net/2263/30088 http://upetd.up.ac.za/thesis/available/etd-12042006-123908/ © 1999, 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 | Operator algebras Linear algebraic groups UCTD Riesz theory and Fredholm determinants in Banach algebras |
| title | Riesz theory and Fredholm determinants in Banach algebras |
| title_full | Riesz theory and Fredholm determinants in Banach algebras |
| title_fullStr | Riesz theory and Fredholm determinants in Banach algebras |
| title_full_unstemmed | Riesz theory and Fredholm determinants in Banach algebras |
| title_short | Riesz theory and Fredholm determinants in Banach algebras |
| title_sort | riesz theory and fredholm determinants in banach algebras |
| topic | Operator algebras Linear algebraic groups UCTD |
| url | http://hdl.handle.net/2263/30088 http://upetd.up.ac.za/thesis/available/etd-12042006-123908/ |