The stochastic Weiss conjecture for bounded analytic semigroups
2013; Wiley; Volume: 88; Issue: 1 Linguagem: Inglês
10.1112/jlms/jdt003
ISSN1469-7750
AutoresJamil Abreu, Bernhard H. Haak, Jan van Neerven,
Tópico(s)Holomorphic and Operator Theory
ResumoJournal of the London Mathematical SocietyVolume 88, Issue 1 p. 181-201 Articles The stochastic Weiss conjecture for bounded analytic semigroups Jamil Abreu, Corresponding Author Jamil Abreu j.m.a.m.vanneerven@tudelft.nl Instituto de Matemática, Estatística e Computaç ao Científica, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, Brazil, jamil@ime.unicamp.brj.m.a.m.vanneerven@tudelft.nlSearch for more papers by this authorBernhard Haak, Bernhard Haak Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, Cours de la Libération, F-33405 Talence cedex, France, bernhard.haak@math.u-bordeaux1.frSearch for more papers by this authorJan van Neerven, Jan van Neerven Delft Institute of Applied Mathematics, Delft University of Technology, PO Box 5031, 2600 GA Delft, The NetherlandsSearch for more papers by this author Jamil Abreu, Corresponding Author Jamil Abreu j.m.a.m.vanneerven@tudelft.nl Instituto de Matemática, Estatística e Computaç ao Científica, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo 13083-859, Brazil, jamil@ime.unicamp.brj.m.a.m.vanneerven@tudelft.nlSearch for more papers by this authorBernhard Haak, Bernhard Haak Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, Cours de la Libération, F-33405 Talence cedex, France, bernhard.haak@math.u-bordeaux1.frSearch for more papers by this authorJan van Neerven, Jan van Neerven Delft Institute of Applied Mathematics, Delft University of Technology, PO Box 5031, 2600 GA Delft, The NetherlandsSearch for more papers by this author First published: 13 March 2013 https://doi.org/10.1112/jlms/jdt003 2010 Mathematics Subject Classification 93B28 (primary), 35R15, 46B09, 47B10, 47D06 (secondary). The first author was supported by FAPESP project 2007/08220-9. The second author was partially supported by the ANR project ANR-09-BLAN-0058-01. The third author was supported by VICI subsidy 639.033.604 of the Netherlands Organisation for Scientific Research (NWO). AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Suppose −A admits a bounded H∞-calculus of angle less than π/2 on a Banach space E which has Pisier's property (α), let B be a bounded linear operator from a Hilbert space H into the extrapolation space E−1 of E with respect to A, and let WH denote an H-cylindrical Brownian motion. Let γ(H, E) denote the space of all γ-radonifying operators from H to E. We prove that the following assertions are equivalent: the stochastic Cauchy problem dU(t) = AU(t) dt + B dWH(t) admits an invariant measure on E; (−A)−1/2 B ∈ γ(H, E); the Gaussian sum ∑n∈ℤ γn 2n/2 R(2n, A)B converges in γ(H, E) in probability. This solves the stochastic Weiss conjecture of [8]. Volume88, Issue1August 2013Pages 181-201 RelatedInformation
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