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Unique ergodicity in C*-dynamical systems
Dissertation (MSc)--University of Pretoria, 2013.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2014
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| _version_ | 1867613522738806784 |
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| access_status_str | Open Access |
| author2 | Duvenhage, Rocco |
| author_browse | Duvenhage, Rocco |
| author_facet | Duvenhage, Rocco |
| collection | Thesis |
| dc_rights_str_mv | © 2013 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, 2013. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/40335 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:29.594Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| 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:2263/40335 Unique ergodicity in C*-dynamical systems Duvenhage, Rocco danie.vanwyk@up.ac.za Stroh, Anton Van Wyk, Daniel Willem C*-dynamical systems Unique ergodicity UCTD Dissertation (MSc)--University of Pretoria, 2013. The aim of this dissertation is to investigate ergodic properties, in particular unique ergodicity, in a noncommutative setting, that is in C*-dynamical systems. Fairly recently Abadie and Dykema introduced a broader notion of unique ergodicity, namely relative unique ergodicity. Our main focus shall be to present their result for arbitrary abelian groups containing a F lner sequence, and thus generalizing the Z-action dealt with by Abadie and Dykema, and also to present examples of C*-dynamical systems that exhibit variations of these (uniquely) ergodic notions. Abadie and Dykema gives some characterizations of relative unique ergodicity, and among them they state that a C*-dynamical system that is relatively uniquely ergodic has a conditional expectation onto the xed point space under the automorphism in question, which is given by the limit of some ergodic averages. This is possible due to a result by Tomiyama which states that any norm one projection of a C*-algebra onto a C*-subalgebra is a conditional expectation. Hence the rst chapter is devoted to the proof of Tomiyama's result, after which some examples of C*-dynamical systems are considered. In the last chapter we deal with unique and relative unique ergodicity in C*-dynamical systems, and look at examples that illustrate these notions. Speci cally, we present two examples of C*-dynamical systems that are uniquely ergodic, one with an R2-action and the other with a Z-action, an example of a C*-dynamical system that is relatively uniquely ergodic but not uniquely ergodic, and lastly an example of a C*-dynamical system that is ergodic, but not uniquely ergodic. gm2014 Mathematics and Applied Mathematics unrestricted 2014-06-24T09:36:13Z 2014-06-24T09:36:13Z 2014-04-23 2013 Dissertation Van Wyk, DW 2013, Unique ergodicity in C*-dynamical systems, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/40335> E14/4/186/gm http://hdl.handle.net/2263/40335 en © 2013 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 | C*-dynamical systems Unique ergodicity UCTD Unique ergodicity in C*-dynamical systems |
| title | Unique ergodicity in C*-dynamical systems |
| title_full | Unique ergodicity in C*-dynamical systems |
| title_fullStr | Unique ergodicity in C*-dynamical systems |
| title_full_unstemmed | Unique ergodicity in C*-dynamical systems |
| title_short | Unique ergodicity in C*-dynamical systems |
| title_sort | unique ergodicity in c dynamical systems |
| topic | C*-dynamical systems Unique ergodicity UCTD |
| url | http://hdl.handle.net/2263/40335 |