Some estimates for non-microstates free entropy dimension, with applications to $q$-semicircular families
| dc.creator | Shlyakhtenko, Dimitri | |
| dc.date | 2003-08-10 | |
| dc.date.accessioned | 2026-07-07T05:00:18Z | |
| dc.date.available | 2026-07-07T05:00:18Z | |
| dc.description | We give an general estimate for the non-microstates free entropy dimension $δ^{*}(X_{1},..., X_{n})$. If $X_{1},..., X_{n}$ generate a diffuse von Neumann algebra, we prove that $δ^{*}(X_{1},..., X_{n})\geq 1$. In the case that $X_{1},..., X_{n}$ are $q$-semicircular variables as introduced by Bozejko and Speicher and $q^{2}n<1$, we show that $δ^{*}(X_{1},..., X_{n})>1$. We also show that for $|q|<\sqrt{2}-1$, the von Neumann algebras generated by a finite family of $q$-Gaussian random variables satisfy a condition of Ozawa and are therefore solid: the relative commutant of any diffuse subalgebra must be hyperfinite. In particular, when these algebras are factors, they are prime and do not have property $Γ$. | |
| dc.identifier | https://arxiv.org/abs/math/0308093 | |
| dc.identifier | http://arxiv.org/abs/math/0308093 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68287 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54 | |
| dc.title | Some estimates for non-microstates free entropy dimension, with applications to $q$-semicircular families | |
| dc.type | text |