On the relation of closed forms and Trotterʹs 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 Trotterʹs 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 etA it is possible to introduce an equivalent scalar product on the space, such that etA becomes non-quasi-contractive with respect to the new scalar product.