Relations amongst the distances between $C^{*}$-subalgebras and some canonically associated operator algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910794800693248 |
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| author | Gupta, Ved Prakash Kumar, Sumit |
| author_facet | Gupta, Ved Prakash Kumar, Sumit |
| contents | We prove that the Christensen distance (resp., the Kadison-Kastler distance) between two $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of a $C^*$-algebra $\mathcal{C}$ is equal to that between their enveloping von Neumann algebras $\mathcal{A}^{**}$ and $\mathcal{B}^{**}$ (resp., the tensor product algebras $\mathcal{A} \otimes^{\min} \mathcal{D}$ and $\mathcal{B} \otimes^{\min} \mathcal{D}$, for any unital commutative $C^*$-algebra $\mathcal{D}$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relations amongst the distances between $C^{*}$-subalgebras and some canonically associated operator algebras Gupta, Ved Prakash Kumar, Sumit Operator Algebras 46L05, 47L40, 46M05 We prove that the Christensen distance (resp., the Kadison-Kastler distance) between two $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of a $C^*$-algebra $\mathcal{C}$ is equal to that between their enveloping von Neumann algebras $\mathcal{A}^{**}$ and $\mathcal{B}^{**}$ (resp., the tensor product algebras $\mathcal{A} \otimes^{\min} \mathcal{D}$ and $\mathcal{B} \otimes^{\min} \mathcal{D}$, for any unital commutative $C^*$-algebra $\mathcal{D}$). |
| title | Relations amongst the distances between $C^{*}$-subalgebras and some canonically associated operator algebras |
| topic | Operator Algebras 46L05, 47L40, 46M05 |
| url | https://arxiv.org/abs/2501.13039 |