  The spinless Falicov-Kimball model on the simple cubic lattice is analyzed in
the Hubbard-I and dynamical mean field (DMFT) approximations. The Matsubara and
real frequency itinerant electron Green's functions, the evolution of the
system with doping, and the range of phase separation are found in two
approximations. At large values of the on-site Coulomb repulsion both
approximations give similar results. The phase separation can be also favorable
for a more general model, where heavy electrons have a finite bandwidth. This
indicates that the phase separation phenomenon is an inherent feature of the
systems described by the Hubbard-like models with wide and narrow bands.
