A stochastic Datko–Pazy theorem

Let H be a Hilbert space and E a Banach space. In this note we present a sufficient condition for an operator to be γ-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.