For an infinite-dimensional Lie group $G$ modeled on a locally convex Lie algebra ${\\mathfrak{g}}$ , we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie group extension $G^{\\sharp}$ of $G$ . (The main point is the smooth structure on $G^{\\sharp}$ .) For infinite-dimensional Lie groups $G$ which are $1$ -connected, regular, and modeled on a barreled Lie algebra ${\\mathfrak{g}}$ , we characterize the unitary ${\\mathfrak{g}}$ -represe…