  The aim of this paper is to give a characterization in Hilbert spaces of the
generators of $C_0$-semigroups associated with closed, sectorial forms in terms
of the convergence of a generalized Trotter's product formula. In the course of
the proof of the main result we also present a similarity result which can be
of independent interest: for any unbounded generator $A$ of a $C_0$-semigroup
$e^{tA}$ it is possible to introduce an equivalent scalar product on the space,
such that $e^{tA}$ becomes non-quasi-contractive with respect to the new scalar
product.
