Browsing Theses and Dissertations (Mathematics and Applied Mathematics) by Supervisor "Duvenhage, Rocco"

Browsing Theses and Dissertations (Mathematics and Applied Mathematics) by Supervisor "Duvenhage, Rocco"

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  • Ergodic properties of noncommutative dynamical systems 
    Snyman, Mathys Machiel (University of Pretoria, 2013)
    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, ...
  • Joinings and relative ergodic properties of W*-dynamical systems 
    King, Malcolm Bruce (University of Pretoria, 2019)
    We prove a characterization of relative weak mixing in W*-dynamical systems in terms of a relatively independent joining. We then define a noncommutative version of relative discrete spectrum, show that it generalizes both ...
  • A structure theorem for asymptotically abelian W*-dynamical systems 
    King, Malcolm Bruce (University of Pretoria, 2016)
    We prove a partial non-commutative analogue of the Furstenberg-Zimmerman Structure Theorem, originally proved by Tim Austin, Tanya Eisner and Terence Tao. In Chapter 1, we review the GNS construction for states on von ...
  • The Szemerédi property in noncommutative dynamical systems 
    Beyers, Frederik Johannes Conradie (University of Pretoria, 2009-06-02)
    No abstract available. Copyright 2008, 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 ...
  • Unique ergodicity in C*-dynamical systems 
    Van Wyk, Daniel Willem (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 ...