A new approach to the similarity problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910397061136384 |
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| author | Papapetros, E. |
| author_facet | Papapetros, E. |
| contents | We say that a $C^*$-algebra $\mathcal{A}$ satisfies the similarity property ((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to \mathcal{B}(\mathit{H})$, where $\mathit{H}$ is a Hilbert space, is similar to a $*$-homomorphism. We introduce the following hypothesis (EP). (EP): Every separably acting von Neumann algebra with a cyclic vector is hyperreflexive. We prove that under (EP), all $C^*$-algebras satisfy (SP). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new approach to the similarity problem Papapetros, E. Operator Algebras We say that a $C^*$-algebra $\mathcal{A}$ satisfies the similarity property ((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to \mathcal{B}(\mathit{H})$, where $\mathit{H}$ is a Hilbert space, is similar to a $*$-homomorphism. We introduce the following hypothesis (EP). (EP): Every separably acting von Neumann algebra with a cyclic vector is hyperreflexive. We prove that under (EP), all $C^*$-algebras satisfy (SP). |
| title | A new approach to the similarity problem |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2403.19668 |