Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917701765562368 |
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| author | Mai, Tobias Speicher, Roland |
| author_facet | Mai, Tobias Speicher, Roland |
| contents | We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a lower bound by Garg, Gurvits, Oliveira, and Widgerson on this capacity, by making it dimension-independent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates Mai, Tobias Speicher, Roland Operator Algebras Functional Analysis Rings and Algebras We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a lower bound by Garg, Gurvits, Oliveira, and Widgerson on this capacity, by making it dimension-independent. |
| title | Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates |
| topic | Operator Algebras Functional Analysis Rings and Algebras |
| url | https://arxiv.org/abs/2406.15922 |