The authors consider a Kolmogorov operator \(L_0\) in a Hilbert space H, related to a stochastic PDE with a singular quasi-dissipative drift \(F\) defined on a suitable space of regular functions. The authors prove that \(L_0\) is essentially \(m\)-dissipative in the space \(L^p\) with respect to a family of measures \(\nu_t\) that of the Fokker-Planck equation given by \(L_0\). This result implies that \(L_0\) generates a Markov \(C_0\) semigroup. A uniqueness result is also proved. Such results generalize previous ones obtained by the authors in the case of finite-dimensional spaces.