Trotter-Kato Product Formulæ: Operator-Norm Topology

After strong convergence (Chap. 5 ), we elucidate in this and the next chapter one of the main topics of the present book. It concerns different results on convergence of the Trotter and the Trotter-Kato product formulæ in the operator-norm topology with, and without, operator-norm error-bound estimates of the rate of convergence. Trotter-Kato product formulæoperator-norm convergenceself-adjoint semigroups Similarly to Chap. 5 , we focus on the case where generators A and B for a couple of \(C_0\) -semigroups are non-negative self-adjoint operators in a separable Hilbert space \(\mathfrak {H}\) . The principal results are (relatively) recent, and they essentially are in many aspects attributable to the authors of this book; see Notes to Chap. 6 .