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

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