Hyperreflexivity of von Neumann algebras and similarity of finitely generated $C^*$-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915626342154240 |
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| author | Eleftherakis, G. K. Paulsen, V. I. |
| author_facet | Eleftherakis, G. K. Paulsen, V. I. |
| contents | Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive algebras by projections. We prove that our third hypothesis is equivalent to every finitely generated C*-algebra satisfying the SP.
We show that to prove that every von Neumann algebra is hyperreflexive it is enough to show that when one extends a hyperreflexive algebra by a single projection it remains hyperreflexive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperreflexivity of von Neumann algebras and similarity of finitely generated $C^*$-algebras Eleftherakis, G. K. Paulsen, V. I. Operator Algebras Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive algebras by projections. We prove that our third hypothesis is equivalent to every finitely generated C*-algebra satisfying the SP. We show that to prove that every von Neumann algebra is hyperreflexive it is enough to show that when one extends a hyperreflexive algebra by a single projection it remains hyperreflexive. |
| title | Hyperreflexivity of von Neumann algebras and similarity of finitely generated $C^*$-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2505.08720 |