Logarithmic Sobolev Inequalities and Spectral Gaps: Perturbation Theory

We prove the logarithmic Sobolev inequality for a diffusion operator on the Wiener space. The operator we consider is a perturbation of the Ornstein-Uhlenbeck operator. We use the logarithmic Sobolev inequality for the Ornstein-Uhlenbeck operator. Our method is based on Dirichlet forms and it can be applied to more general diffusions.