On the Ornstein-Uhlenbeck Operators on Wiener-Riemannian Manifolds

In this paper, we study the properties of infinite-dimensional Ornstein-Uhlenbeck operators on submanifolds in Wiener spaces. We establish the hypoellipticity of the Laplacians acting on the space of tensors. By using this, we show the essential selfadjointness of the Laplacians acting on the space of 0-forms, i.e., function spaces.