Inductive limits of compact quantum metric spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910890092134400 |
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| author | Long, Botao Sadeghi, Ghadir |
| author_facet | Long, Botao Sadeghi, Ghadir |
| contents | A compact quantum metric space is a unital $C^*$-algebra equipped with a Lip-norm. Let $\{(A_n, L_n)\}$ be a sequence of compact quantum metric spaces, and let $ϕ_n:A_n\to A_{n+1}$ be a unital $^*$-homomorphism preserving Lipschitz elements for $n\geq 1$. We show that there exists a compact quantum metric space structure on the inductive limit $\varinjlim(A_n,ϕ_n)$ by means of the inverse limit of the state spaces $\{\mathcal{S}(A_n)\}$. We also give some sufficient conditions that two inductive limits of compact quantum metric spaces are Lipschitz isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18266 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inductive limits of compact quantum metric spaces Long, Botao Sadeghi, Ghadir Operator Algebras 46L85(Primary) 46L87, 58B34(Secondary) A compact quantum metric space is a unital $C^*$-algebra equipped with a Lip-norm. Let $\{(A_n, L_n)\}$ be a sequence of compact quantum metric spaces, and let $ϕ_n:A_n\to A_{n+1}$ be a unital $^*$-homomorphism preserving Lipschitz elements for $n\geq 1$. We show that there exists a compact quantum metric space structure on the inductive limit $\varinjlim(A_n,ϕ_n)$ by means of the inverse limit of the state spaces $\{\mathcal{S}(A_n)\}$. We also give some sufficient conditions that two inductive limits of compact quantum metric spaces are Lipschitz isomorphic. |
| title | Inductive limits of compact quantum metric spaces |
| topic | Operator Algebras 46L85(Primary) 46L87, 58B34(Secondary) |
| url | https://arxiv.org/abs/2503.18266 |