  A resolution of the identity due to canonical coherent states is often proven
in the weak operator topology. However, such a resolution with an integral
symbol is typically supposed to hold in the strong operator topology associated
with the framework of the spectral theorem. We provide an elementary proof of
the strong convergence for the resolution of the identity due to canonical
coherent states starting with a mostly familiar setup. Further, we enjoy a
different proof and show that the relevant uniform limit does not exist.
