Continuous extension of a densely parameterized semigroup

Let be a dense sub-semigroup of ℝ₊, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over can be extended to a weakly continuous semigroup over ℝ₊. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which are extendable to semigroups over ℝ₊. O.M. Shalit was partially supported by the Gutwirth Fellowship.