Proceedings of the American Mathematical Society

Fixed point property and normal structure for Banach spaces associated to locally compact groups

Author(s): Anthony To-ming Lau; Peter F. Mah; Ali Ülger
Journal: Proc. Amer. Math. Soc. 125 (1997), 2021-2027.
MSC (1991): Primary 43A10, 43A15, 46B20, 47H09, 22D10; Secondary 54G12
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Abstract: In this paper we investigate when various Banach spaces associated to a locally compact group $G$

have the fixed point property for nonexpansive mappings or normal structure. We give sufficient conditions and some necessary conditions about $G$

for the Fourier and Fourier-Stieltjes algebras to have the fixed point property. We also show that if a $C^{*}$ -algebra $\mathfrak {A}$ has the fixed point property then for any normal element $a$

of $\mathfrak {A}$ , the spectrum $\sigma (a)$ is countable and that the group $C^{*}$ -algebra $C^{*}(G)$ has weak normal structure if and only if $G$

is finite.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A10, 43A15, 46B20, 47H09, 22D10, 54G12

Anthony To-ming Lau
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

Peter F. Mah
Affiliation: Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada, P7B 5E1
Email: pfmah@cs-acad-lan.lakeheadu.ca

Ali Ülger
Affiliation: Department of Mathematics, Koc University, 80860-Istinye, Istanbul, Turkey
Email: aulger@ku.edu.tr

DOI: 10.1090/S0002-9939-97-03773-8
PII: S 0002-9939(97)03773-8
Keywords: Locally compact groups, Fourier and Fourier-Stieltjes algebras, group algebra, $C^{*}$-algebra, fixed point property, weak-normal structure, uniformly Kadec-Klee property, Radon Nikodym property
Received by editor(s): August 29, 1995
Received by editor(s) in revised form: January 19, 1996
Additional Notes: The first author's research was supported by an NSERC grant and the third author's research was supported by TUBA
Communicated by: J. Marshall Ash
Copyright of article: Copyright 1997, American Mathematical Society

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