Weakly almost periodic functionals on certain Banach algebras

Abstract

For a Lau algebra A, we study the Banach space WAP(A) of all weakly almost periodic functionals on A to obtain some equivalent conditions for the exis-tence of topological left invariant means on a topological left introverted subspace X of A contained in WAP(A). Finally, we consider relations between the existence of a topological left invariant mean on X and a common xed point property.

Mathematics Subject Classication (2010): Primary 43A60, 46H05; Secondary 43A07, 46L10, 47L10.

Key words: Lau algebra, left invariant mean, left introverted subspace, semi-topological
semigroup, weakly almost periodic functional.