HAAK, Bernhard H.; VAN NEERVEN, Jan

doi:10.7153/oam-06-50

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HAAK, Bernhard H.
Institut de Mathématiques de Bordeaux [IMB]

VAN NEERVEN, Jan
Delft Institute of Applied Mathematics [TWA]

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Operators and Matrices. 2012, vol. 6, n° 4, p. 767-792

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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.< Leer menos

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Uniformly gamma-radonifying families of operators and the stochastic Weiss conjecture

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