Let S be a suitable subsemigroup of a locally compact abelian group and let \(\textbf{T}=\left\{ T\left( s\right) \right\} _{s\in S}\) be a bounded and strongly continuous representation of S on a Hilbert space H. Assume that unitary spectrum of \(\textbf{T}\) is contained in a Helson set. We show that if the function \(\left( s,t\right) \rightarrow \langle T\left( s\right) x,T\left( t\right) x\rangle \) vanishes at infinity for some \(x\in H\) , then \(\lim _{s}{|} T\left( s\right) x{|} =0.\)
