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Characterization theorems in von Neumann algebras
Dissertation (MSc)--University of Pretoria, 1990.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613526992879616 |
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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, 1990. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/85284 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:33.559Z |
| 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:2263/85284 Characterization theorems in von Neumann algebras Stroh, Anton Kriek, Carel G. UCTD Characterization theorems von Neumann algebras Dissertation (MSc)--University of Pretoria, 1990. The aim of this thesis is to study the characterization theorems in von Neumann algebras. This class of operator algebras was defined for the first time in 1930 by J von Neumann in terms of a representation on a Hilbert space. After the studies of Gelfand, Naimark and Segal, von Neumann algebras were defined as *-subalgebras of bounded operators on a Hilbert space which are weak operator closed. Von Neumann himself was intrigued by the question how to characterize van Neumann algebras in a more abstract, hence representation- independent way. By studying the features of von Neumann algebras, Kadison and Sakai almost simultaneously solved this problem in the mid-fifties. Chapter one contains important results on projections and operators that are needed to prove the characterization theorems later. The well-know spectral theory and a few important facts on Borel calculus are also stated here. By using a theorem of Baire we extend the Gelfand-Naimark *- isomorphism to a *- homomorphism between all the bounded complex Borel functions on the spectrum of an operator T and the von Neumann algebra generated by T and I. Mathematics and Applied Mathematics MSc Unrestricted 2022-05-17T11:19:51Z 2022-05-17T11:19:51Z 2021/10/06 1990 Dissertation * https://repository.up.ac.za/handle/2263/85284 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 Characterization theorems von Neumann algebras Characterization theorems in von Neumann algebras |
| title | Characterization theorems in von Neumann algebras |
| title_full | Characterization theorems in von Neumann algebras |
| title_fullStr | Characterization theorems in von Neumann algebras |
| title_full_unstemmed | Characterization theorems in von Neumann algebras |
| title_short | Characterization theorems in von Neumann algebras |
| title_sort | characterization theorems in von neumann algebras |
| topic | UCTD Characterization theorems von Neumann algebras |
| url | https://repository.up.ac.za/handle/2263/85284 |