Hi,

Let $G$ be a LC group and $T:L^{2}(G)\longrightarrow L^{2}(G)$ be
a bdd operator. Also assume that $\alpha\in Aut(G)$. I think that
$$T(f\circ\alpha)=T(f)\circ\alpha.$$
But I Cann't proof or disproof it. Even a reference to the proof
will help. Thanks