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A stochastic Datko-Pazy theorem

Bernhard Haak·Jan van Neerven·Mark Veraar
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Abstract

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 $γ$--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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Bernhard Haak, Jan van Neerven, Mark Veraar. 2006-08-14. A stochastic Datko-Pazy theorem. https://arxiv.org/abs/math/0602427

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