Abstract. In this paper, a characterization for continuous functions on (0, ∞) to be the Laplace transforms of f ∈ L ∞ (0, ∞) is obtained. It is also shown that the vector-valued version of this characterization holds if and only if the underlying Banach space has the Radon-Nikodým property. Using these characterizations, some results, different from that of the Hille-Yosida theorem, on generators of semigroups of operators are obtained.

Abstract. It is shown that a normed vector lattice (E, · ) is order continuous if and only if, for every lattice norm ρ on E with ρ ≤ · , the · -topology and ρ-topology coincide on every order interval of E.