Differentiable perturbations of Ornstein-Uhlenbeck operators. [arXiv:0705.3126v1]

... $f:H\to \Rset$, where $H$ is a separable Hilbert space. We consider a perturbation of the form $N_0\phi=L\phi+ < D\phi,F>$ where $F:H\to H$ is bounded and Fr\'echet differentiable with uniformly continuous and bounded differential. Hence, we prove that $N_0$ is $m$-dissipative and its closure in $C_b(H)$ coincides with the infinitesimal generator of a diffusion semigroup ...