A stochastic Datko–Pazy theorem☆

@inproceedings{Haak2006ASD,
  title={A stochastic Datko–Pazy theorem☆},
  author={Bernhard H. Haak and Jan van Neerven and Mark Veraar},
  year={2006}
}
Let H be a Hilbert space and E a Banach space. In this note we present a sufficient condition for an operator R : H → 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. 
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