ERA

Download the full-sized PDF of Strongly amenable semigroups and nonlinear fixed point propertiesDownload the full-sized PDF

Analytics

Share

Permanent link (DOI): https://doi.org/10.7939/R3Q39T

Download

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Graduate Studies and Research, Faculty of

Collections

This file is in the following collections:

Theses and Dissertations

Strongly amenable semigroups and nonlinear fixed point properties Open Access

Descriptions

Other title
Subject/Keyword
semigroups
amenability
fixed point
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Bouffard, Nicolas
Supervisor and department
Lau, Anthony To-Ming (Mathematical and statistical sciences)
Examining committee member and department
Al-Hussein, Mohamed (Civil and Environmental engineering)
Dai, Feng (Mathematical and statistical sciences)
Poliquin, René (Mathematical and statistical sciences)
Troitsky, Vladimir (Mathematical and statistical sciences)
Sims, Brailey (School of mathematical and physical sciences, University of Newcastle, Australia)
Department
Department of Mathematical and Statistical Sciences
Specialization

Date accepted
2011-08-29T16:20:43Z
Graduation date
2011-11
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Left amenability, in it's modern form, was introduced by M. M. Day, in the 1940s. Amenability of groups and semigroups turned out to be quite common, and many interesting results are known, which motivated the introduction of extreme left amenability by Granirer in the 1960s. Extreme amenability turn out to be equivalent to a very strong nonlinear fixed point property, but examples of topological groups having this property are rather hard to construct. The purpose of this thesis is to study an intermediate property that we call strong left amenability. If S is a semi-topological semigroup, and A denotes either AP(S), WAP(S) or LUC(S) (the spaces of almost periodic, weakly almost periodic or left uniformly continuous functions on S respectively), then we say that A is strongly left amenable (SLA) if there is a compact left ideal group in the spectrum of A. We then say that S is SLA if LUC(S) is SLA. The first part of the thesis investigates the structure of such semigroups. We give some elementary properties, and characterize those semigroups for AP(S), WAP(S) and LUC(S). We also characterize the strong left amenability of a semigroup when S is discrete, compact or connected. Finally, we show that homomorphic images of an SLA semigroup is SLA and so is the product of an extremely left amenable semigroup by a compact group. We conclude the first part of the thesis by giving some examples. Amenability in general is closely related to non linear fixed point properties, and strong amenability is no exception. In the second part of this thesis, we characterize strong amenability in terms of a fixed compact set. We then obtain various fixed point properties related to jointly continuous actions and non-expansive mappings. We then extend some results on ultimately non-expansive mappings, a concept introduced by Kiang and Edelstein, to right reversible semigroups, and show that one of the conditions is always satisfied when the semigroup is indeed strongly amenable.
Language
English
DOI
doi:10.7939/R3Q39T
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. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. 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.
Citation for previous publication

File Details

Date Uploaded
Date Modified
2014-05-01T01:56:15.217+00:00
Audit Status
Audits have not yet been run on this file.
Characterization
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 1588545
Last modified: 2015:10:12 16:43:55-06:00
Filename: Bouffard_Nicolas_Fall 2011.pdf
Original checksum: 6917d418603c2151d6bab76929a3a966
Well formed: true
Valid: true
Page count: 70
Activity of users you follow
User Activity Date