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Permanent link (DOI): https://doi.org/10.7939/R35D8NM0H
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Some geometric properties on Banach spaces associated to hypergroups. Open Access
- Other title
Geometric properties on Banach spaces
- Type of item
- Degree grantor
University of Alberta
- Author or creator
- Supervisor and department
Anthony To-Ming Lau
- Examining committee member and department
Schmuland, Byron (Mathematical and Statistical Sciences)
Troitsky, Vladimir (Mathematical and Statistical Sciences)
Taylor, Keith F. (Mathematics and Statistics, Dalhousie University)
Wong, Yau Shu (Mathematical and Statistical Sciences)
Lau, Anthony To-Ming (Mathematical and Statistical Sciences)
Dai, Feng (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
- Date accepted
- Graduation date
Doctor of Philosophy
- Degree level
This thesis is dedicated to the study of some geometric properties on Banach spaces associated to hypergroups. This thesis contains three major parts.
The purpose of the first part is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K), and C0(K), the class of left translation invariant W*-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C*-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces.
The second part consists of two themes; fixed point properties for non-expansive and affine maps. The first theme provides a condition when a non-expansive self map on a weak (weak*) compact convex subset of several function spaces over K has a fixed point while the second theme present some applications of common fixed point properties for affine actions of K.
The main concentration of the third part is on initiating the study of inner amenable hypergroups extending amenable hypergroups and inner amenable locally compact groups.
- 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.
- Citation for previous publication
N. Tahmasebi, Hypergroups and invariant complemented subspaces. J. Math. Anal. Appl. 414, 2014, no. 2, 641-655.
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