Spectra of elements in the range of strongly continuous unitary representations of Lie groups (Q438604)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Spectra of elements in the range of strongly continuous unitary representations of Lie groups |
scientific article; zbMATH DE number 6062077
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectra of elements in the range of strongly continuous unitary representations of Lie groups |
scientific article; zbMATH DE number 6062077 |
Statements
Spectra of elements in the range of strongly continuous unitary representations of Lie groups (English)
0 references
31 July 2012
0 references
Consider a strongly continuous unitary representation of a Lie group. The following dichotomy is proved in this paper: The representation is norm continuous, or on an open neighbourhood of the unit there is a residual set of elements whose range admits the entire unit circle as spectrum. The above open neighbourhood is the whole group in the case of a weakly exponential Lie group.
0 references
spectra
0 references
linear operators
0 references
strongly continuous linear representation
0 references
Lie groups
0 references
