Weak and strong approximation of semigroups on Hilbert spaces
Ralph Chill, A. F. M. ter Elst · arXiv (Cornell University) · 2016
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators, in the weak operator topology, in the strong operator topology or in certain integral norms are equivalent under certain natural assumptions which are frequently met in applications.