On the extensions of infinite-dimensional representations of Lie semigroups (Q1607834)

Let \(G\) denote a connected Lie group, \(L(G)\) its Lie algebra and \(exp: L(G) \to G\) its exponential function. For a closed subsemigroup \(S\) of \(G\) its tangent wedge is defined by \(L(S) = \{ X \in L(G):\exp(\mathbb R^+ X) \subseteq S \}\). Necessary and sufficient conditions are obtained for the extendability of a Banach representation of a generating Lie semigroup \(S\) to a local representation of the Lie group generated by \(S\) (i.e. \(L(S)\) is the smallest Lie algebra containing \(L(G))\).