A new regularity result for Ornstein-Uhlenbeck generators and applications

Abstract

Let H be a separable real Hilbert space (norm $\left|\cdot\right|$, inner product $\left\langle{\cdot,\cdot}\right\rangle$). We are given a linear operator $A:D\left( A \right) \subset H \to H$ such that HYPOTHESIS 1.1.

• (i) A is self-adjoint and there exists ω > 0 such that

  $$ \left\langle {Ax,x} \right\rangle \leqslant - \omega {\left| x \right|^2}, x \in D(A). $$

  (1.1)

• (ii) A ⁻¹ is of trace class.

Dedicated to Philippe Bénilan