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

摘要

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