A note on finite-dimensional quotients and the problem of automatic continuity for twisted convolution algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912647344029696 |
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| author | Flores, Felipe I. |
| author_facet | Flores, Felipe I. |
| contents | In this note, we will show that the twisted convolution algebra $L^1_{α,ω}({\sf G},\mathfrak A)$ associated to a twisted action of a locally compact group ${\sf G}$ on a $C^*$-algebra $\mathfrak A$ has the following property: Every quotient by a closed two-sided ideal of finite codimension produces a semisimple algebra. Afterward, we use this property, together with results by H. Dales and G. Willis, to extend previous results by the author and to produce large classes of examples of algebras with automatic continuity properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on finite-dimensional quotients and the problem of automatic continuity for twisted convolution algebras Flores, Felipe I. Functional Analysis Operator Algebras Primary 43A20, Secondary 47L65, 46H40 In this note, we will show that the twisted convolution algebra $L^1_{α,ω}({\sf G},\mathfrak A)$ associated to a twisted action of a locally compact group ${\sf G}$ on a $C^*$-algebra $\mathfrak A$ has the following property: Every quotient by a closed two-sided ideal of finite codimension produces a semisimple algebra. Afterward, we use this property, together with results by H. Dales and G. Willis, to extend previous results by the author and to produce large classes of examples of algebras with automatic continuity properties. |
| title | A note on finite-dimensional quotients and the problem of automatic continuity for twisted convolution algebras |
| topic | Functional Analysis Operator Algebras Primary 43A20, Secondary 47L65, 46H40 |
| url | https://arxiv.org/abs/2410.12162 |