  In this paper we introduce a class of pseudo-dissipative holomorphic maps
which contains, in particular, the class of infinitesimal generators of
semigroups of holomorphic maps on the unit ball of a complex Banach space. We
give a growth estimate for maps of this class. In particular, it follows that
pseudo-dissipative maps on the unit ball of (infinite-dimensional) Banach
spaces are bounded on each domain strictly contained inside the ball. We also
present some applications.
