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

Lau, Anthony; Mah, Peter; Ülger, Ali

doi:10.1090/S0002-9939-97-03773-8

Fixed point property and normal structure for Banach spaces associated to locally compact groups
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by Anthony To-ming Lau, Peter F. Mah and Ali Ülger

Proc. Amer. Math. Soc. 125 (1997), 2021-2027

DOI: https://doi.org/10.1090/S0002-9939-97-03773-8

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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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