Exercise 8, § 1

Let $\mathbf{T}$ be given the normalized Haar and $\mathscr{L}(L^2(\mathbf{T}))$ the normic topology. Show that the regular representation of $\mathbf{T}$ on $L^2(\mathbf{T})$ is not continuous. (For all $g \in \mathbf{T}$ distinct from e, construct a function $f \in L^2(\mathbf{T})$ such that $\|f\| = 1$, $\|\gamma(g)f - f\| = \sqrt{2}$.)