On the relation of closed forms and Trotter's product formula

The aim of this paper is to give a characterization in Hilbert spaces of the generators of C₀-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 C₀-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.