  We give a simple, straightforward proof of the non-hypercyclicity of an
arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as
well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials,
which, under a certain condition on the spectrum of $A$, coincides with the
$C_0$-semigroup generated by it. We also establish non-hypercyclicity for
symmetric operators.
