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

Authors: Anthony To-ming Lau, Peter F. Mah and Ali Ülger
Journal: Proc. Amer. Math. Soc. 125 (1997), 2021-2027
MSC (1991): Primary 43A10, 43A15, 46B20, 47H09, 22D10; Secondary 54G12
MathSciNet review: 1372037
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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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Additional Information

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

Ali Ülger
Affiliation: Department of Mathematics, Koc University, 80860-Istinye, Istanbul, Turkey

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
Article copyright: © Copyright 1997 American Mathematical Society

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