  We study non-recurrence sets for weakly mixing dynamical systems by using
linear dynamical systems. These are systems consisting of a bounded linear
operator acting on a separable complex Banach space X, which becomes a
probability space when endowed with a non-degenerate Gaussian measure. We
generalize some recent results of Bergelson, del Junco, Lema\'nczyk and
Rosenblatt, and show in particular that sets \{n_k\} such that n_{k+1}/{n_k}
tends to infinity, or such that n_{k} divides n_{k+1} for each k, are
non-recurrence sets for weakly mixing linear dynamical systems. We also give
examples, for each r, of r-Bohr sets which are non-recurrence sets for some
weakly mixing systems.
