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Topological Invariant Means and Action of Locally Compact Semitopological Semigroups Open Access

Descriptions

Other title
Subject/Keyword
topological stationary
topological invariant means
topological lumpy
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Huang, Qianhong
Supervisor and department
Anthony To- Ming Lau
Examining committee member and department
Vladimir G. Troitsky
Anthony To- Ming Lau
Vladyslav Yaskin
Michael Y. Li
Byron Schmuland
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2015-09-24T15:23:21Z
Graduation date
2015-11
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R30K26K6G
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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