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Characterisations of Pseudo-Amenability
thesis
posted on 2023-09-25, 02:08 authored by Vujičić, AleksaWe start this thesis by introducing the theory of locally compact groups and their associated Haar measures. We provide examples and prove important results about locally compact and more specifically amenable groups. One such result is known as the Følner condition, which characterises the class amenable groups. We then use this characterisation to define the notion of a pseudo-amenable group. Our central theorem that we present provides new characterisations of pseudo-amenable groups. These characterisations allows us to prove several new results about these groups, which closely mimic well known results about amenable groups. For instance, we show that pseudo-amenability is preserved under closed subgroups and homomorphisms.
History
Copyright Date
2019-01-01Date of Award
2019-01-01Publisher
Te Herenga Waka—Victoria University of WellingtonRights License
CC BY-SA 4.0Degree Discipline
MathematicsDegree Grantor
Te Herenga Waka—Victoria University of WellingtonDegree Level
MastersDegree Name
Master of ScienceANZSRC Type Of Activity code
1 PURE BASIC RESEARCHVictoria University of Wellington Item Type
Awarded Research Masters ThesisLanguage
en_NZVictoria University of Wellington School
School of Mathematics and StatisticsAdvisors
Pham, HungUsage metrics
Keywords
AmenabilityPseudo-amenabilityHaar measureLocally compact groupBanach-Tarski paradoxFølner conditionParadoxical decompositionFunctional analysisLebesgue spaceBorel regular measureSchool: School of Mathematics and Statistics010106 Lie Groups, Harmonic and Fourier Analysis010108 Operator Algebras and Functional Analysis970101 Expanding Knowledge in the Mathematical SciencesDegree Discipline: MathematicsDegree Level: MastersDegree Name: Master of ScienceLie Groups, Harmonic and Fourier AnalysisOperator Algebras and Functional Analysis