Extension of unitary representations of inductive limits of finite dimensional Lie groups
The author proves that every continuous unitary representation of the inductive limit \[ GL({\mathbb{Z}},{\mathbb{R}})=\lim_{\vec n}GL(2n+1,{\mathbb{R}}) \] of general linear groups can be extended by continuity to the unitary representation of a Hilbert-Lie group \(GL_ 2(a)\) (which depends on the starting representation) with \[ GL({\mathbb{Z}},{\mathbb{R}})=\lim_{\vec a}GL_ 2(a). \]
scientific article; zbMATH DE number 4146295
scientific article