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Topological centers and topologically invariant means related to locally compact groups

  • Author / Creator
    Chan, Pak-Keung
  • In this thesis, we discuss two separate topics from the theory of harmonic analysis on locally compact groups. The first topic revolves around the topological centers of module actions induced by unitary representations while the second one deals with the set of topologically invariant means associated to an amenable representation. Part I of this thesis is about the topological centers of bilinear maps induced by unitary representations. We give a characterization when the center is minimal in term of a factorization property. We give conditions which guarantee that the center is maximal. Various examples whose topological centers are maximal, minimal nor neither will be given. We also investigate the topological centers related to sub-representations, direct sums and tensor products. In Part II we study of the set of topologically invariant means associated to an amenable representation. We construct topologically invariant means for an amenable representation by two different methods. A lower bound of the cardinality of the set of topologically invariant means will be given.

  • Subjects / Keywords
  • Graduation date
    2010-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3R06Z
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Lau, Anthony To-Ming (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Safouhi, Hassan (Campus Saint-Jean)
    • Dai, Feng (Department of Mathematical and Statistical Sciences)
    • Neufang, Matthias (School of Mathematics and Statistics, Carleton University)
    • Schmuland, Byron (Department of Mathematical and Statistical Sciences)
    • Runde, Volker (Department of Mathematical and Statistical Sciences)