Finite speed of propagation and off-diagonal bounds for Ornstein?Uhlenbeck operators in infinite dimensions

We study the Hodge–Dirac operators (Formula presented.) associated with a class of non-symmetric Ornstein–Uhlenbeck operators (Formula presented.) in infinite dimensions. For (Formula presented.) we prove that (Formula presented.) generates a (Formula presented.)-group in (Formula presented.) with respect to the invariant measure if and only if (Formula presented.) and (Formula presented.) is self-adjoint. An explicit representation of this (Formula presented.)-group in (Formula presented.) is given, and we prove that it has finite speed of propagation. Furthermore, we prove (Formula presented.) off-diagonal estimates for various operators associated with (Formula presented.), both in the self-adjoint and the non-self-adjoint case