  We study the existence of global implicit functions for equations defined on
open subsets of Banach spaces. The partial derivative with respect to the
second variable is only required to have a left inverse instead of being
invertible. Generalizing known results, we provide sufficient criteria which
are easy to check. These conditions essentially rely on the existence of
diffeomorphisms between the respective projections of the set of zeros and
appropriate Banach spaces, as well as a corresponding growth bound. The
projections further allow to consider cases where the global implicit function
is not defined on all of the open subset corresponding to the first variable.
