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The weighted compactification of a locally compact group and topological centres

  • Author / Creator
    Mazowita, Matthew C
  • Let G be a locally compact group. It is well-known that G^LUC, the spectrum of the algebra of left uniformly continuous functions on G, the so-called LUC-compactification of G, is a semigroup with product restricted from the Arens product on LUC(G)^*. Now consider the algebra of weighted left uniformly continuous functions on G, LUC(G,w^-1). The spectrum G^LUC_w is a compactification of G homeomorphic to G^LUC, but is not a semigroup unless the weight is a homomorphism (in which case G^LUC_w = \G^LUC). We study the algebraic and topological properties of G^LUC_w and the semigroup it generates in [0,1]G^LUC_w, including characterizing when it is dense, and use the results to attempt to extend some topological centre and determination results for G^LUC of Budak, Isik, and Pym to G^LUC_w and present some partial results. We also partially characterize the isometric isomorphisms of Beurling (weighted group) algebras. Finally, we show that the topological centre of the Fourier algebra of the Fell group is strongly Arens irregular.

  • Subjects / Keywords
  • Graduation date
    2014-06
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R31N7XT7P
  • 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)
    • Tony Lau (Math and Stats)
  • Examining committee members and their departments
    • N. Tomczak-Jaegerman (Math and Stats)
    • Vladimir Troitsky (Math and Stats)
    • Feng Dai (Math and Stats)
    • Byron Schmuland (Math and Stats)