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Yamamoto type theorems in Banach algebras
Dissertation (MSc)--University of Pretoria, 1995.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613519845785600 |
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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 | © 2020 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)--University of Pretoria, 1995. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/85538 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:26.754Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| 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:2263/85538 Yamamoto type theorems in Banach algebras Stroh, Anton Swart, Johan Bapela, Manas Majakwane UCTD Yamamoto theorems Banach algebras Dissertation (MSc)--University of Pretoria, 1995. The aim of this thesis is to study the asymptotic relation between the approximation numbers and isolated spectral points with finite multiplicity in a general Banach algebra setting. In 1967 T. Yamamoto was the first to show that such asymptotic results hold for the algebra of n by n matrices with entries in the complex field. About twenty years later Edmunds and Evans found a meaningful extension of Yamamoto' s Theorem for bounded operators on a Banach space. After an extensive study of the notion of finite rank elements, we extend Yamamoto's Theorem to a general Banach algebra setting. Recently, Nylen and Rodman proved a special case of the result by showing that Yamamoto's Theorem holds for Banach algebras with the spectral radius property and conjectured that any Banach algebra possesses this property. In this thesis we prove their conjecture in the affirmative. Mathematics and Applied Mathematics MSc Unrestricted 2022-05-17T11:22:25Z 2022-05-17T11:22:25Z 2021/10/22 1995 Dissertation * https://repository.up.ac.za/handle/2263/85538 en © 2020 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 | UCTD Yamamoto theorems Banach algebras Yamamoto type theorems in Banach algebras |
| title | Yamamoto type theorems in Banach algebras |
| title_full | Yamamoto type theorems in Banach algebras |
| title_fullStr | Yamamoto type theorems in Banach algebras |
| title_full_unstemmed | Yamamoto type theorems in Banach algebras |
| title_short | Yamamoto type theorems in Banach algebras |
| title_sort | yamamoto type theorems in banach algebras |
| topic | UCTD Yamamoto theorems Banach algebras |
| url | https://repository.up.ac.za/handle/2263/85538 |