A stochastic Datko-Pazy theorem

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

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Functional Analysis, 47D06; 28C20; 46B09; 46B15; 47N30

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http://salesiana.dossiersoluciones.com/handle/123456789/109035

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0602427
 http://arxiv.org/abs/math/0602427

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arXiv