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.
