  The Hubbard model in the limit of infinite $U$ is investigated within a
projected slave fermion representation and following a previous work of the
author and collaborators \cite{BFK}. The stability of the Nagaoka's phase with
respect to a non vanishing concentration of holes ($\delta_h$) is analyzed by
envisaging the existence of a spin effective action for itinerant magnetism of
the Hubbard model. It is considered that,as the hole doping increases away from
the half filled insulating limit, free holes are expected to be more
delocalized. Depending on treatment for the hopping: a ferromagnetic or
anti-ferromagnetic ordering might arise and the Nagaoka's phase might have some
stability with respect to $\delta_h \neq 0$.
