Topological centers and topologically invariant means related to locally compact groups Open Access
- Other title
Locally compact groups
Differentiable dynamical systems -- Mathematical models
- Type of item
- Degree grantor
University of Alberta
- Author or creator
- Supervisor and department
Lau, Anthony To-Ming (Department of Mathematical and Statistical Sciences)
- Examining committee member and department
Schmuland, Byron (Department of Mathematical and Statistical Sciences)
Safouhi, Hassan (Campus Saint-Jean)
Dai, Feng (Department of Mathematical and Statistical Sciences)
Neufang, Matthias (School of Mathematics and Statistics, Carleton University)
Runde, Volker (Department of Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
- Date accepted
- Graduation date
Doctor of Philosophy
- Degree level
In this thesis, we discuss two separate topics from the theory of harmonic analysis on locally compact groups.
The first topic revolves around the topological centers of module actions induced by unitary representations while the second one deals with the set of topologically invariant means associated to an amenable representation.
Part I of this thesis is about the topological centers of bilinear maps induced by unitary representations.
We give a characterization when the center is minimal in term of a factorization property.
We give conditions which guarantee that the center is maximal.
Various examples whose topological centers are maximal, minimal nor neither will be given.
We also investigate the topological centers related to sub-representations, direct sums and tensor products.
In Part II we study of the set of topologically invariant means associated to an amenable representation.
We construct topologically invariant means for an amenable representation by two different methods.
A lower bound of the cardinality of the set of topologically invariant means will be given.
- 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.
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