ANGELA ALBANESE and FRANZISKA KÜHNEMUND
Trotter-Kato approximation theorems for locally equicontinuous semigroups
Pages: 19-53
Received: 29 November 2001
Revised: 14 May 2002
Mathematics Subject Classification (2000): 47D03 - 47A58 - 35k65
Abstract: 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.