## Some results about dissipativity of Kolmogorov operators.(English)Zbl 0996.47028

Summary: Given a Hilbert space $$H$$ with a Borel probability measure $$\nu$$, we prove the $$m$$-dissipativity in $$L^1(H, \nu)$$ of a Kolmogorov operator $$K$$ that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.

### MSC:

 47B25 Linear symmetric and selfadjoint operators (unbounded) 81S20 Stochastic quantization 37L40 Invariant measures for infinite-dimensional dissipative dynamical systems 35K57 Reaction-diffusion equations 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
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### References:

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