Moore groups have the \(WS\)-property (Q1209275)

The authors show that in Moore groups for every weakly almost periodic function \(f\) we have \(\{f_ g^ h(x)=f(hxg)\), \(h,g\in G\}\) forms a weakly relative compact subset of \(C(G)\) (bounded continuous functions). As a consequence it follows that in Moore groups there exist strongly well distributed sequences. (This follows then already from the in other respects much more general Theorem 3 (or Corollary) by \textit{V. Losert} and \textit{H. Rindler} [Invent. Math. 50, 65-74 (1978; Zbl 0414.22006)]).