Lie generators for semigroups of transforms on a Polish space, Electron

Abstract. Let X be a separable complete metric space. We characterize completely the innitesimal generators of semigroups of linear transformations in Cb(X), the bounded real-valued continuous functions on X, that are induced by strongly continuous semigroups of continuous transformations in X. In order to do this, Cb(X) is equipped with a locally convex topology known as the strict topology. Introduction. A strongly continuous semigroup of transformations on a topological space X is a function T from [0;1) into the collection of continuous transformations from X into X such that (1) T (0) = I, the identity transformation on X, (2) T (t) T (s) = T (t+ s) for all t; s 0, an