  Let $H$ be a Hilbert space and $E$ a Banach space. In this note we present a
sufficient condition for an operator $R: H\to E$ to be $\gamma$--radonifying in
terms of Riesz sequences in $H$. This result is applied to recover a result of
Lutz Weis and the second named author on the $R$-boundedness of resolvents,
which is used to obtain a Datko-Pazy type theorem for the stochastic Cauchy
problem. We also present some perturbation results.
