$B$-valued semi-circular system and the free Poincaré inequality
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912333311246336 |
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| author | Ito, Hyuga |
| author_facet | Ito, Hyuga |
| contents | We characterize $B$-valued semi-circular system in terms of $B$-valued free probabilistic analogue of Poincaré inequality. This is a $B$-valued generalization of Biane's theorem \cite[Theorem 5.1]{b03}. Moreover, we prove that Voiculescu's conjecture on $B$-valued free Poincaré inequality in \cite{aim06} is not in the affirmative as it is. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $B$-valued semi-circular system and the free Poincaré inequality Ito, Hyuga Operator Algebras Rings and Algebras We characterize $B$-valued semi-circular system in terms of $B$-valued free probabilistic analogue of Poincaré inequality. This is a $B$-valued generalization of Biane's theorem \cite[Theorem 5.1]{b03}. Moreover, we prove that Voiculescu's conjecture on $B$-valued free Poincaré inequality in \cite{aim06} is not in the affirmative as it is. |
| title | $B$-valued semi-circular system and the free Poincaré inequality |
| topic | Operator Algebras Rings and Algebras |
| url | https://arxiv.org/abs/2409.16498 |