Trotter-Kato approximation theorems for locally equicontinuous semigroups

In this paper we prove Trotter-Kato approximation results and the Lie-Trotter product formula for locally equicontinuous semigroups on sequentially complete locally convex spaces. These results are then applied to the Ornstein-Uhlenbeck semigroup on the space of bounded continuous functions on Rn endowed with a locally convex topology agreeing with the compact-open topology on norm-bounded sets.