Every Semitopological Semigroup Compactification of the Group H₊[0, 1] is Trivial

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.