We review the various assumptions under which abstract versions of the quan
tum mechanical virial theorem have been proved, We point out a relationship
between the virial theorem for a pair of operators HI A and the regularity
properties of the map R There Exists s --> e(isA) (z - H)(-1)e(isA). We gi
ve an example showing that the statement of the virial theorem in [CFKS] is
incorrect.