This is an announcement for the paper "A stochastic Datko-Pazy theorem" by Bernhard Haak, Jan van Neerven and Mark Veraar.

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 $\ga$--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.

Archive classification: Functional Analysis

Mathematics Subject Classification: 47D06; 28C20; 46B09; 46B15; 47N30

Remarks: 10 pages

The source file(s), Haak-vanNeerven-Veraar-arxiv.tex: 33344 bytes, is(are) stored in gzipped form as 0602427.gz with size 10kb. The corresponding postcript file has gzipped size 60kb.

Submitted from: bernhard.haak@math.uni-karlsruhe.de

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