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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.01574 |
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| _version_ | 1866914833783324672 |
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| author | Melnikov, Vasily |
| author_facet | Melnikov, Vasily |
| contents | Let $M$ be a $W^{\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\mathscr{B}(H)$ factors through an $\mathfrak{L}_{\infty}$-space only if $M$ is a finite type $\mathrm{I}$ algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism Melnikov, Vasily Functional Analysis Operator Algebras 46B20, 46L10 Let $M$ be a $W^{\ast}$-algebra acting on a separable complex Hilbert space $H$. We show that the inclusion of $M$ into $\mathscr{B}(H)$ factors through an $\mathfrak{L}_{\infty}$-space only if $M$ is a finite type $\mathrm{I}$ algebra. |
| title | On $\mathfrak{L}_{\infty}$-liftings of the Gelfand-Naimark morphism |
| topic | Functional Analysis Operator Algebras 46B20, 46L10 |
| url | https://arxiv.org/abs/2403.01574 |