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

  • Topological lumpy
  • Topological stationary
  • Topological invariant means

• Graduation date

  Fall 2015

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R30K26K6G

• 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.