We combine harmonic analysis and operator algebraic techniques to give a concise argument that the left regular representation of a locally compact group is cyclic if and only if the group is first countable, a result first proved by Greenleaf and Moskowitz.
"Cyclicity of the left regular representation of a locally compact group." Rocky Mountain J. Math. 48 (3) 1015 - 1018, 2018. https://doi.org/10.1216/RMJ-2018-48-3-1015