Unitary Product Formulæ

In this chapter, we first recollect the main results about convergence of the unitary Trotter product formula in the strong operator topology, Sect. 13.1. Then we focus on sufficient conditions ensuring convergence of the unitary Trotter–Kato product formula in a more general set-up, which involves a new topology of convergence. In contrast to the operator-norm convergent unitary Trotter product formula (Sect. 13.2), we scrutinise in Sect. 13.3 a convergence of the unitary Trotter–Kato product formula for holomorphic Kato functions in topology of the locally convex Fréchet space. We note that for a class of admissible Kato functions, the convergence of the unitary Trotter–Kato product formula occurs in the strong operator topology