Extension of unitary representations of inductive limits of finite dimensional Lie groups (Q912994)
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scientific article; zbMATH DE number 4146295
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extension of unitary representations of inductive limits of finite dimensional Lie groups |
scientific article; zbMATH DE number 4146295 |
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Extension of unitary representations of inductive limits of finite dimensional Lie groups (English)
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1988
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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 \[ GL({\mathbb{Z}},{\mathbb{R}})=\lim_{\vec a}GL_ 2(a). \]
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continuous unitary representation
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inductive limit
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general linear groups
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Hilbert-Lie group
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