This is an announcement for the paper "Uniformly gamma-radonifying families of operators and the linear stochastic Cauchy problem in Banach spaces" by Bernhard Haak and Jan van Neerven.

Abstract: We introduce the notion of uniform $\gamma$--radonification of a family of operators, which unifies the notions of $R$--boundedness of a family of operators and $\gamma$--radonification of an individual operator. We study the the properties of uniformly $\gamma$--radonifying families of operators in detail and apply our results to the stochastic abstract Cauchy problem $$ dU(t) = AU(t),dt + B,dW(t), \quad U(0)=0. $$ Here, $A$ is the generator of a strongly continuous semigroup of operators on a Banach space $E$, $B$ is a bounded linear operator from a separable Hilbert space $H$ into $E$, and $W_H$ is an $H$--cylindrical Brownian motion.

Archive classification: Functional Analysis

Mathematics Subject Classification: 47B10; 35R15; 46B09; 46B50; 47D06; 60B11; 60H15

Remarks: submitted for publication

The source file(s), unif-gamma.arxiv.tex: 75863 bytes, is(are) stored in gzipped form as 0611724.gz with size 23kb. The corresponding postcript file has gzipped size 152kb.

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/0611724

or

http://arXiv.org/abs/math.FA/0611724

or by email in unzipped form by transmitting an empty message with subject line

uget 0611724

or in gzipped form by using subject line

get 0611724

to: math@arXiv.org.