  We investigate the subject of speed of mixing for operators on infinite
dimensional Hilbert spaces which are strongly mixing with respect to a
nondegenerate Gaussian measure. We prove that there is no way to find a uniform
speed of mixing for all square-integrable functions. We give classes of regular
functions for which the sequence of correlations decreases to zero with speed
$n^{-\alpha}$ when the eigenvectors associated to unimodular eigenvalues of the
operator are parametrized by an $\alpha$-H\"olderian $\mathbb{T}$-eigenvector
field.
