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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.03677 |
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| _version_ | 1866909177002065920 |
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| author | Ozawa, Narutaka |
| author_facet | Ozawa, Narutaka |
| contents | We answer the recent problem posed by Baudier, Braga, Farah, Vignati, and Willett that asks whether the $\ell_\infty$-direct sum of the matrix algebras embeds into the uniform Roe algebra or the quasi-local algebra of a uniformly locally finite metric space. The answers are no and yes, respectively. Hence the inclusion of the uniform Roe algebra into the quasi-local algebra can be proper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03677 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Embeddings of matrix algebras into uniform Roe algebras and quasi-local algebras Ozawa, Narutaka Operator Algebras Functional Analysis 47C15, 46L05, 05C48 We answer the recent problem posed by Baudier, Braga, Farah, Vignati, and Willett that asks whether the $\ell_\infty$-direct sum of the matrix algebras embeds into the uniform Roe algebra or the quasi-local algebra of a uniformly locally finite metric space. The answers are no and yes, respectively. Hence the inclusion of the uniform Roe algebra into the quasi-local algebra can be proper. |
| title | Embeddings of matrix algebras into uniform Roe algebras and quasi-local algebras |
| topic | Operator Algebras Functional Analysis 47C15, 46L05, 05C48 |
| url | https://arxiv.org/abs/2310.03677 |