Every semitopological semigroup compactification of the group H + [0,1] is trivial

Abstract

Let G=H+[0, 1] be the topological group of all orientation-preserving selfhomeomorphisms of the closed interval [0,1] endowed with the usual compact open topology. We show that every weakly almost periodic function on G is constant. Consequently, G does not admit nontrivial (weakly) continuous representations by linear isometries in reflexive Banach spaces.