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
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0602427
or
http://arXiv.org/abs/math.FA/0602427
or by email in unzipped form by transmitting an empty message with subject line
uget 0602427
or in gzipped form by using subject line
get 0602427
to: math@arXiv.org.