In this dissertation we develop aspects of ergodic theory
for C*-dynamical systems for which the C*-algebras are allowed
to be noncommutative. We define four ergodic properties,
with analogues in classic ergodic theory, and study C*-dynamical
systems possessing these properties. Our analysis will show that, as
in the classical case, only certain combinations of these properties
are permissable on C*-dynamical systems. In the second half of
this work, we construct concrete noncommutative C*-dynamical
systems having various permissable combinations of the ergodic
properties. This shows that, as in classical ergodic theory, these
ergodic properties continue to be meaningful in the noncommutative
case, and can be useful to classify and analyse C*-dynamical
systems. / Dissertation (MSc)--University of Pretoria, 2013. / gm2014 / Mathematics and Applied Mathematics / unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/40351 |
| Date | January 2013 |
| Creators | Snyman, Mathys Machiel |
| Contributors | Duvenhage, Rocco, mmsnyman@gmail.com, Stroh, Anton |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Rights | © 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. |
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