2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109035Let $H$ 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 $γ$--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.Updated version, 9 pages. To appear in J. Math. Anal. ApplFunctional Analysis47D06; 28C20; 46B09; 46B15; 47N30text