The space of contractive $C_{0}$-semigroups is a Baire space

Abstract

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C0-semigroups under the topology of uniform weak convergence on compact subsets of R`. Eisner, Mátrai, Serény, et al. raised in various publications 2008-10 the open problem: Does this space constitute a Baire space? Observing that the subspace of unitary semigroups is completely metrisable and appealing to known density results, we solve this problem by showing that certain topological properties can in general be transferred from dense subspaces to larger spaces.