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^LUCw is a compactification of G homeomorphic to G^LUC, but is not a semigroup unless the weight is a homomorphism (in which case G^LUCw = \G^LUC). We study the algebraic and topological properties of G^LUCw and the semigroup it generates in [0,1]G^LUCw, 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

  • Topological centre
  • Beurling algebra

• Graduation date

  Spring 2014

• 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.