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Amenability of Discrete Semigroup Flows Open Access

Descriptions

Other title
Subject/Keyword
Abstract Harmonic Analysis
flows
semigroup
stone
amenability
density
cech
discrete
compactification
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Loliencar, Prachi
Supervisor and department
Lau, Anthony To-Ming (Mathematical and Statistical Sciences)
Examining committee member and department
Troitsky, Vladimir G. (Mathematical and Statistical Sciences)
Lewis, James D. (Mathematical and Statistical Sciences)
Li, Michael Y. (Mathematical and Statistical Sciences)
Runde, Volker (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2015-09-30T09:30:47Z
Graduation date
2015-11
Degree
Master of Science
Degree level
Master's
Abstract
A discrete flow (S,X) is a semigroup S acting on a set X where both S, and X are equipped with the discrete topology. Amenability of semigroups is a topic that explores the existence of measures that are invariant under the semigroup multiplication. The goal of this thesis is to generalize these results to a semigroup acting on a set, i.e. a flow, so that the invariance is with respect to the action. We start out in Chapter 1 by giving some preliminaries that are important for the results in this thesis. Chapter 2 generalizes basic theorems characterizing amenability and gives sufficient and necessary conditions for the same. We discuss some relevant topics such as the Hahn-Banach extension theorem and an application of flow amenability - a fixed point theorem. Next, in Chapter 3, we discuss various Folner conditions - combinatorial properties that characterize aspects of amenability. Finally, in Chapter 4, we discuss the flow stucture of the Stone-Cech compactification of a flow. We then discuss the concept of density of means and apply some properties of Folner nets. In Chapter 5 we briefly get into reversible invariance - a property that is equivalent to amenability in groups (and group flows).
Language
English
DOI
doi:10.7939/R37W67D8D
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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