Abstract:In this paper we show that the Fourier-Stieltjes algebra B(G) of a non-compact locally compact group G cannot have the weak * fixed point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989. We also show that a locally compact group is compact exactly if the asymptotic centre of any non-empty weak * closed bounded convex subset C in B(G) with respect to a decreasing net of bounded subsets is a non-empty norm compact subset. In particular, when G … Show more
“…Geometry and nonlinear fixed-point properties. In the paper [8], the authors show that the Fourier-Stieltjes algebra B(G) of a noncompact locally compact group G cannot have the weak * -weak * fixed-point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989.…”
Section: Multipliers Of Commutative Banach Algebras With Applications Tomentioning
“…Geometry and nonlinear fixed-point properties. In the paper [8], the authors show that the Fourier-Stieltjes algebra B(G) of a noncompact locally compact group G cannot have the weak * -weak * fixed-point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989.…”
Section: Multipliers Of Commutative Banach Algebras With Applications Tomentioning
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