ON THE BEST APPROXIMATION OF THE INFINITESIMAL GENERATOR OF A CONTRACTION SEMIGROUP IN A HILBERT SPACE

Elena E. Berdysheva     (Department of Mathematics, Justus Liebig University Giessen, Germany)
Maria A. Filatova     (Ural Federal University; Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, Ekaterinburg,, Russian Federation)

Abstract


Let \(A\) be the infinitesimal generator  of a strongly continuous contraction semigroup in a  Hilbert space \(H\).   We give an upper estimate for the best approximation of the operator \(A\) by bounded linear operators with a prescribed norm  in the space \(H\) on the class \(Q_2 = \{x\in \mathcal{D}(A^2) : \|A^2 x\| \leq 1\}\),  where \(\mathcal D(A^2)\) denotes the domain of \(A^2\).


Keywords


Contraction semigroup, Infinitesimal generator, Stechkin’s problem

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References


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DOI: http://dx.doi.org/10.15826/umj.2017.2.006

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