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On the best approximation of the infinitesimal generator of a contraction semigroup in a Hilbert space. (English) Zbl 1448.41025

Summary: 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 \(A^2\).

MSC:

41A50 Best approximation, Chebyshev systems
47J25 Iterative procedures involving nonlinear operators
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References:

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