This is an announcement for the paper “Weak* fixed point property for the Reduced Fourier-Stieltjes algebra of a separable locally compact group” by Fouad Naderihttps://arxiv.org/find/math/1/au:+Naderi_F/0/1/0/all/0/1.
Abstract: In this paper we show that if the reduced Fourier-Stieltjes algebra $B_p(G)$ of a separable locally compact group has either weak$^*$ fixed point property or asymptotic center property, then $G$ is compact. These give affirmative answers to open problems raised in [G. Fendler, A. T. Lau, and M. Leinert, {\it Weak$^*$ fixed point property and and asymptotic center for the Fourier-Stieltjes algebra of a locally compact group,} J. Funct. Anal. 264 (1) (2013), 288-302.] Our theorem helps us to provide a negative answer to a question posed by Randrianantoanina. We also show that for a compact scattered topological space $X$, the C$^*$-algebra $C(X)$ has weak fixed point property. This gives a positive answer to a problem posed by Lau and et al.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1612.08286