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 ∈ D(A 2 ) : A 2 x ≤ 1}, where D(A 2 ) denotes the domain of A 2 .