  In this paper we show that the realization in $L^p(X,\nu_\infty)$ of the
nonsymmetric Ornstein-Uhlenbeck operator $L$ is sectorial for any
$p\in(1,+\infty)$ and we provide an explicit sector of analyticity. Here
$(X,\mu_\infty,H_\infty)$ is an abstract Wiener space, i.e., $X$ is a separable
Banach space, $\mu_\infty$ is a centred non degenerate Gaussian measure on $X$
and $H_\infty$ is the associated Cameron-Martin space. Further, $\nu_\infty$ is
a weighted Gaussian measure, that is, $\nu_\infty=e^{-U}\mu_\infty$ where $U$
is a convex function which satisfies some minimal conditions. Our results
strongly rely on the theory of nonsymmetric Dirichlet forms and on the
divergence form of the realization of $L$ in $L^2(X,\nu_\infty)$.
