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

Abstract

In this paper we investigate when various Danach 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 21 has the fixed point property then for any normal element a of 21, the spectrum a (a) is countable and that the group C*-algebra C* (G) has weak normal structure if and only if G is finite. © 1997 American Mathematical Society.