The ideal separation property for reduced group $C^*$-algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912257367080960 |
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| author | Austad, Are Thiel, Hannes |
| author_facet | Austad, Are Thiel, Hannes |
| contents | We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view of harmonic analysis and noncommutative geometry. We establish several permanence properties of locally compact groups for which $L^1(G) \subseteq C^*_{\mathrm{red}}(G)$ has the ideal separation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14880 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The ideal separation property for reduced group $C^*$-algebras Austad, Are Thiel, Hannes Operator Algebras Functional Analysis Group Theory Primary 22D15, 43A20, 46H10, Secondary 22D20, 22D25, 46L05 We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view of harmonic analysis and noncommutative geometry. We establish several permanence properties of locally compact groups for which $L^1(G) \subseteq C^*_{\mathrm{red}}(G)$ has the ideal separation property. |
| title | The ideal separation property for reduced group $C^*$-algebras |
| topic | Operator Algebras Functional Analysis Group Theory Primary 22D15, 43A20, 46H10, Secondary 22D20, 22D25, 46L05 |
| url | https://arxiv.org/abs/2408.14880 |