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Operator amenability of ultrapowers of the Fourier algebra

  • Author / Creator
    Schlitt, Kyle J
  • It has been shown by Matthew Daws that the group algebra of a discrete group is never ultra-amenable. We explore the weak analogue to this statement and demonstrate that if any commutative group algebra is ultra-weakly amenable, then the underlying group must necessarily be discrete. By showing that ultrapowers of complete maximal operator spaces are themselves maximal, we are able to demonstrate that the assumption of ultra-operator amenability of the Fourier algebra A(G) forces G to be discrete. By considering a wide class of discrete groups, we find sufficient evidence to make reasonable the conjecture that such a property may well force G to be finite. We conclude with consideration of another weak analogue, showing that ultra-weak operator amenability of A(G) already forces G to be discrete.

  • Subjects / Keywords
  • Graduation date
    2017-11:Fall 2017
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R34F1MZ2X
  • 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
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Volker Runde (Mathematics)
  • Examining committee members and their departments
    • Alexander Litvak (Mathematics)
    • Vladimir Troitsky (Mathematics)
    • Jochen Kuttler (Mathematics)
    • Douglas Farenick (Mathematics)