A stochastic Datko-Pazy theorem

Details A stochastic Datko-Pazy theorem A stochastic Datko-Pazy theorem

2006-02-20

arxiv.org/abs/math/0602427v2

Mathematics

Functional Analysis

Updated version, 9 pages. To appear in J. Math. Anal. Appl

Scientific paper

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.

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