Continuous extension of a densely parameterized semigroup (Q1014258)

The authors consider a weakly continuous semigroup \(T=\{T_s\}_{s\in S}\) of linear operators on a separable reflexive Banach space, defined over some dense sub-semigroup \(S\subset\mathbb R_+\). It is shown that this semigroup admits a weakly continuous extension to a semigroup over \(\mathbb R_+\). A similar result is also proved for nonlinear nonexpansive semigroups. As a corollary, the authors characterize all densely parametrized semigroups which are extendable to semigroups over \(\mathbb R_+\).