ERA

Download the full-sized PDF of Ergodic theorems for certain Banach algebras associated to locally compact groupsDownload the full-sized PDF

Actions

Download  |  Analytics

Export to: EndNote  |  Zotero  |  Mendeley

Communities

This file is in the following communities:

Faculty of Graduate Studies and Research

Collections

This file is in the following collections:

Theses and Dissertations

Ergodic theorems for certain Banach algebras associated to locally compact groups Open Access

Descriptions

Other title
Subject/Keyword
locally compact group
ϕ-amenability
Figà-Talamanca-Herz algebra
norm spectrum
ergodic multiplier
representation
ergodic sequence
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Guex, Sébastien M.
Supervisor and department
Lau, Anthony To-Ming (Mathematical and Statistical Sciences)
Examining committee member and department
Troitsky, Vladimir (Mathematical and Statistical Sciences)
Litvak, Alexander (Mathematical and Statistical Sciences)
Runde, Volker (Mathematical and Statistical Sciences)
Sit, Jeremy (Electrical and Computer Engineering)
Forrest, Brian (Pure Mathematics, Univeristy of Waterloo)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2012-12-11T15:48:17Z
Graduation date
2013-06
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
In this thesis, we establish some ergodic theorems related to Ap(G), the Figà-Talamanca-Herz algebra of a locally compact group G. This thesis is divided in two main portions. The first part is primarily concerned with the study of ergodic sequences in Ap(G) and with a newly introduced notion of ergodic multipliers. After presenting a full description of the non-degenerate *-representations of Ap(G) and of their extensions to the multiplier algebra MAp(G), it is shown that, for all locally compact groups, the weakly ergodic sequences in MAp(G) coincide with the strongly ergodic ones, and that they are, in a sense, approximating sequences for the topologically invariant means on some spaces of linear functionals on Ap(G). Next, motivated by the study of ergodic sequences of iterates, we introduce a notion of ergodic multipliers, and we provide a solution to the dual version of the complete mixing problem for probability measures, The second part is of a more abstract nature and deals with some ergodic and fixed point properties of ϕ-amenable Banach algebras. Among other things, we prove a mean ergodic theorem, establish the uniqueness of a two-sided ϕ-mean on the weakly almost periodic functionals, and provide a simpler proof of a fixed point theorem which is well known in the context of semigroups. We also study the norm spectrum of some linear functionals on Ap(G) and present a new characterization of discrete groups.
Language
English
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
2014-04-24T22:20:06.475+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: 559616
Last modified: 2015:10:12 18:02:19-06:00
Filename: Guex_Sébastien_Spring 2013.pdf
Original checksum: d1b4a8f12ac35886ff2e096e19d096c2
Well formed: false
Valid: false
Status message: Unexpected error in findFonts java.lang.ClassCastException: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject cannot be cast to edu.harvard.hul.ois.jhove.module.pdf.PdfDictionary offset=554160
Page count: 86
Activity of users you follow
User Activity Date