  Model of the degenerated weakly non-ideal Bose gas is considered without
suggestion on C-number representation of the creation and annihilation
operators with zero momentum. The "density-density" correlation function and
the one-particle Green function are calculated on basis of the suggestion about
C-number representation of the operator of particle density in the Bose
condensate. It is shown, that the pole in the "density-density" Green function
determines the Bogolyubov's spectrum of the collective excitations, which have
the phonon-roton form. At the same time the spectrum of the one-particle
excitations possesses a gap, whose value is connected with the density of
particles in the Bose condensate.
