Topological Invariant Means and Action of Locally Compact Semitopological Semigroups

  • Author / Creator
    Huang, Qianhong
  • Let a locally compact semitopological semigroup S have a separately con- tinuous left action on a locally compact Hausdorff X. We define a jointly continuous left action of the measure algebra M(S) on the bounded Borel measure space M(X) which is an analogue of the convolution of measure alge- bras M(S). We further introduce a separately continuous left action of M(S) on the dual of a M(S)-invariant subspace A of M(X)∗ in analogue with Arens product. We consider the fixed point of this action on the set of means on A (topological S-invariant mean on A) and characterize its existence in analogue with topological right stationary, ergodic properties, Dixmier condition etc. A notion of topological (S, A)-lumpy is introduced and its relation with topolog- ical S-invariant mean on A is studied. The relation of existence of topological invariant means on a subspace of X and on X itself is also studied.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • 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
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Anthony To- Ming Lau
  • Examining committee members and their departments
    • Anthony To- Ming Lau
    • Michael Y. Li
    • Byron Schmuland
    • Vladyslav Yaskin
    • Vladimir G. Troitsky