  We give a formulation of classical mechanics in the language of operators
acting on a Hilbert space. The formulation given comes from a unitary
irreducible representation of the Galilei group that is compatible with the
basic postulates of classical mechanics, particularly the absence of an
uncertainty principle between the position and momentum of a particle. It is
shown that the theory exposed in the article contains the Koopman-von Neumann
formalism of classical mechanics as a particular case.
