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@article{faucris.119163924,
abstract = {Let (*G*,*θ*) be a Banach–Lie group with involutive automorphism *θ*, be the *θ*-eigenspaces in the Lie algebra of *G*, and *H*=(*G*^{θ})_{0} be the identity component of its group of fixed points. An Olshanski semigroup is a semigroup *S*⊆*G* of the form , where *W* is an open Ad(*H*)-invariant convex cone in and the polar map is a diffeomorphism. Any such semigroup carries an involution * satisfying . Our central result, generalizing the Lüscher–Mack theorem for finite-dimensional groups, asserts that any locally bounded *-representation with a dense set of smooth vectors defines by “analytic continuation” a unitary representation of the simply connected Lie group *G*_{c} with Lie algebra . We also characterize those unitary representations of *G*_{c} obtained by this construction. With similar methods, we further show that semibounded unitary representations extend to holomorphic representations of complex Olshanski semigroups.},
author = {Merigon, Stephane and Neeb, Karl-Hermann},
doi = {10.1093/imrn/rnr174},
faupublication = {yes},
journal = {International Mathematics Research Notices},
pages = {4260 - 4300},
peerreviewed = {Yes},
title = {{Analytic} extension techniques for unitary representations of {Banach}-{Lie} groups},
volume = {18},
year = {2012}
}