The free entropy dimension of hyperfinite von Neumann algebras
| dc.creator | Jung, Kenley | |
| dc.date | 2001-12-04 | |
| dc.date | 2003-09-13 | |
| dc.date.accessioned | 2026-07-07T04:44:59Z | |
| dc.date.available | 2026-07-07T04:44:59Z | |
| dc.description | Suppose M is a hyperfinite von Neumann algebra with a tracial state $ϕ$ and $\{a_1,...,a_n\}$ is a set of selfadjoint generators for M. We calculate $δ_0(a_1,...,a_n)$, the modified free entropy dimension of $\{a_1,...,a_n\}$. Moreover we show that $δ_0(a_1,...,a_n)$ depends only on M and $ϕ$. Consequently $δ_0(a_1,...,a_n)$ is independent of the choice of generators for M. In the course of the argument we show that if $\{b_1,...,b_n\}$ is a set of selfadjoint generators for a von Neumann algebra R with a tracial state and $\{b_1,...,b_n\}$ has finite dimensional approximants, then for any $b\in R$ $δ_0(b_1,...,b_n)\geq δ_0(b)$. Combined with a result by Voiculescu this implies that if R has a regular diffuse hyperfinite von Neumann subalgebra, then $δ_0(b_1,...,b_n)=1$. | |
| dc.description | 34 pages, minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0112039 | |
| dc.identifier | http://arxiv.org/abs/math/0112039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62816 | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 46L54; Secondary 52C17, 53C30 | |
| dc.title | The free entropy dimension of hyperfinite von Neumann algebras | |
| dc.type | text |