Power Bounded and Weak* fixed point property for Fourier - Stieltjes algebras of locally compact groups

Abstract

We study the Fixed point property a normal structure for subsets of some Banach spaces and an algebras associated with locally compact groups with nonexpansive mappings in spaces of continuous functions. We consider the separation property of positive definite functions on locally compact groups and applications, the ideals with bounded approximate identities and completely bounded homomorphisms of the Fourier algebras. We characterize the invariant means with submeans and fixed point properties for nonexpansive representations of topological semigroups and on Banach spaces with normal structure. We determine the power boundedness, the structure of power bounded elements and the weak* fixed point property and asymptotic centre for the Fourier-Stieltjes algebras of locally compact groups and other commutative Banach algebras.